
	Where results make sense

Topic: Representation theory of the symmetric group

Related Topics

Abd el Kader

Joe Costello

Pipil

William Thomas Sampson

Sehra

In the News (Fri 18 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Group representation - Wikipedia, the free encyclopedia
		Representation theory is the branch of mathematics that studies properties of abstract groups via their representations as linear transformations of vector spaces.
		Representation theory is important because it enables many group-theoretic problems to be reduced to problems in linear algebra, which is a very well-understood theory.
		A representation of a group G on a vector space V over a field K is a group homomorphism from G to GL( V), the general linear group on V.
	en.wikipedia.org /wiki/Group_representation (1503 words)

	Representation theory of the symmetric group - Wikipedia, the free encyclopedia
		In mathematics, the representation theory of the symmetric group is a particular case of the representation theory of finite groups, for which a concrete and detailed theory can be obtained.
		This has a large area of potential applications, from symmetric function theory to problems of quantum mechanics for a number of identical particles.
		Therefore according to the representation theory of a finite group, the number of inequivalent irreducible representations, over the complex numbers, is equal to the number of partitions of n.
	en.wikipedia.org /wiki/Representation_theory_of_the_symmetric_group (167 words)

	Representation Theory (Site not responding. Last check: 2007-11-06)
		This course is an introduction to the representation theory of groups.
		Representation theory studies the way in which a given group may act on vector spaces; in other words, it is concerned with representing groups as groups of matrices.
		The main questions in representation theory are related to: (1) the construction of irreducible representations; (2) the calculation of certain algebraic invariants of these; (3) the decomposition of other representations into irreducibles.
	math.albany.edu:8000 /math/pers/lenart/teach/repres.html (399 words)

	MTH-4E20 : Representation Theory with Advanced Topics
		Representation Theory demonstrates the enormous power of linear algebra and builds upon what students have learned at level 1 and 2 in Pure Mathematics I and II and Algebra I and II.
		Restriction of a representation of a group G to a G -stable subspace.
		Restriction of a representation of a group G to a subgroup.
	www.mth.uea.ac.uk /maths/syllabuses/0001/4E2001.html (590 words)

	Representation Theory Of Symmetric Groups (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		There are in fact two parallel theories here: one for the symmetric groups S n involving the ane Kac-Moody algebra of type A p 1, and one for their double covers b S n involving the twisted algebra of type A p 1.
		210 The representation theory of the symmetric groups (context) - James - 1978
		8 The spin representations of the symmetric group (context) - Morris - 1965
	citeseer.ist.psu.edu /626921.html (624 words)

	Citebase - Affine sl_p controls the representation theory of the symmetric group and related Hecke algebras
		In this paper we prove theorems that describe how the representation theory of the affine Hecke algebra of type A and of related algebras such as the group algebra of the symmetric group are controlled by integrable highest weight representations of the characteristic zero affine Lie algebra \hat{sl}_l.
		Representations of Hecke algebras 45 [R] Rogawski, J. Representations of GL (n) over a p-adic field with an Iwahori-fixed vector.
		We construct categorifications for blocks of symmetric groups and deduce that two blocks are...
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/9907129 (1085 words)

	Symmetric group - Wikipedia, the free encyclopedia
		The representation of a permutation as a product of transpositions is not unique; however, the number of transpositions needed to represent a given permutation is either always even or always odd.
		is a group homomorphism ({+1,-1} is a group under multiplication, where +1 is e, the neutral element).
		can be written as a product of disjoint cycles; this representation is unique up to the order of the factors.
	en.wikipedia.org /wiki/Symmetric_group (482 words)

	Weyl Group Symmetric Functions and the Representation Theory of Lie Algebras - Ram (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		In this case the definition is motivated by the theory of centralizer algebras.
		It is clear from the double centralizer theory that an analogue of the Frobenius characteristic map is a feature of the double...
		Weyl group symmetric functions and the representation theory of Lie algebras.
	citeseer.ist.psu.edu /557364.html (530 words)

	Cambridge University Engineering Dept. - Structures Group (Site not responding. Last check: 2007-11-06)
		Symmetric structures commonly occur in nature and in engineering design due to their optimal load carrying abilities and their aesthetic appeal.
		Group theory is the mathematical language best suited to the description of the symmetry properties of a structure.
		Previous work applied group theory to the stiffness method of structural analysis in order to exploit symmetry properties of the structure and hence simplify the analysis of the induced displacements of the structure.
	www-civ.eng.cam.ac.uk /abstract/kangwaiabs.html (250 words)

	UW Madison Lie Theory Seminar Fall 2003
		For the symmetric groups (and for Weyl groups of type B) the resulting representations are completely classified and contain the irreducible ones.
		Abstract: A symmetric pair is an ordered pair of reductive linear algebraic groups, (G,K) where K is an algebraic subgroup of G consisting of the fixed points of a regular involution on G. In this talk we will emphasis the theory of symmetric pairs as it relates to representation theory.
		A corollary of his result is that the sum of the degrees of the characters of GL(n,q) is equal to the number of symmetric matrices in the group.
	www.math.wisc.edu /~ram/liethy03.html (2578 words)

	Representation Theory of Symmetric Groups (L24) (Site not responding. Last check: 2007-11-06)
		However, we shall not require any background knowledge of representation theory in positive characteristic - the symmetric groups enjoy special properties which mean that their representation theory is best approached in a characteristic-free way, and does not require any technical machinery.
		The representation theory of the symmetric groups is intricately tied up with the polynomial representation theory of general linear groups.
		James and A. Kerber, The representation theory of the symmetric group, Encyclopædia of mathematics and its applications 16, Addison-Wesley.
	www.maths.cam.ac.uk /postgrad/courses/descriptions/node4.html (274 words)

	The Symmetric Group : Representations, Combinatorial Algorithms, and Symmetric Functions (Graduate T: ... (Site not responding. Last check: 2007-11-06)
		This is an introduction to the representation theory of the symmetric group from three different points of view: via general representation theory, via combinatorial algorithms, and via symmetric functions.
		Among these results are Haiman's theory of dual equivalence and the beautiful Novelli-Pak-Stoyanovskii proof of the hook formula (the latter being new to the second edition).
		Group representations; representations of the symmetric group; combinatorial algorithms; symmetric functions; applications and generalizations.
	bookweb.kinokuniya.co.jp /guest/cgi-bin/booksea.cgi?ISBN=0387950672 (312 words)

	Representation Theory and Young Tableaux (Site not responding. Last check: 2007-11-06)
		We shall develop the combinatorics of Young tableaux and see them in action in the algebra of symmetric functions and representations of the symmetric and general linear groups.
		In paricular, we shall discuss some uses of tableaux in the study of the representations of the symmetric group S_n and the general linear group Gl(m,C).
		Representation theory is easy to define: it is the study of the ways in which a given group may act on vector spaces.
	www.public.iastate.edu /~driessel/young-tableaux.html (411 words)

	Category.org - The Online Shopping Center: Books - Group Theory (Site not responding. Last check: 2007-11-06)
		As well as determining the range of possible 'growth types', for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure.
		Howard Georgi is the co-inventor (with Sheldon Glashow) of the SU(5) theory.
		Throughout the emphasis is on Cayley maps: imbeddings of Cayley graphs for finite groups as (possibly branched) covering projections of surface imbeddings of loop graphs with one vertex.
	www.category.org /browse/books/13940/index.html (5872 words)

	Representation Theory Of Symmetric Groups (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Abstract: this article we will give an overview of the new Lie theoretic approach to the p-modular representation theory of the symmetric groups and their double covers that has emerged in the last few years.
		6 The idempotents of the symmetric group and Nakayama's conjec..
		Representations Of The Symmetric Group Are Reducible Over..
	citeseer.lcs.mit.edu /626921.html (624 words)

	The Symmetric Group (Site not responding. Last check: 2007-11-06)
		This book develops the combinatorics of Young tableaux and shows them in action in the algebra of symmetric functions, representations of the symmetric and general linear groups, and the geometry of flag varieties.
		The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters.
		The character tables of many groups are given, including all groups of order less than 32, and all but one of the simple groups of order less than 1000.
	enotalone.com /books/0387950672.html (728 words)

	The Symmetric Group (Bruce E. Sagan) (Site not responding. Last check: 2007-11-06)
		This text is an introduction to the representation theory of the symmetric group from three different points of view: via general representation theory, via combinatorial algorithms, and via symmetric functions.
		This book has 4 chapters.Chapter1 is about general theory of representations of finite group.Chapter2 is about representation of symmetric groups.chapter3 and 4 are about combinatorial topics and symmetric functions.
		Though I haven't read all of the book,I highly recommand this book because this book shows us introductive part of representation theory with easy words.I think it is worth to read for all who are to begin the study of representation theory.
	johnkeyes.com /a/0387950672-the-symmetric-group.html (350 words)

	GAP Manual: 71 The Specht Share Package
		As the (modular) representation theory of these algebras closely resembles that of the (modular) representation theory of the symmetric groups --- indeed, the later is a special case of the former --- many of the combinatorial tools from the representation theory of the symmetric group are included in the package.
		The ``modular'' representation theory of the Iwahori--Hecke algebras of type A was pioneered by Dipper and James [DJ1,DJ2]; here we briefly outline the theory, referring the reader to the references for details.
		is the Hecke algebras analogue of the characteristic of the field in the modular representation theory of finite groups.
	parallel.rz.uni-mannheim.de /gap/htm/CHAP071.htm (7167 words)

	Representations of the Symmetric Group (Site not responding. Last check: 2007-11-06)
		For the symmetric group of degree n the irreducible representations can be indexed by partitions of weight n.
		Given a partition pa of weight n and a permutation pe in a symmetric group of degree n, return the matrix of the seminormal representation for pe, indexed by pa, over the rationals.
		Given a partition pa of weight n and a permutation pe in a symmetric group of degree n, return the matrix of the orthogonal representation for pe, indexed by pa. An orthogonal basis is used to compute the matrix which may have entries in a cyclotomic field.
	www.math.lsu.edu /magma/text981.htm (269 words)

	NONCOMMUTATIVE CHARACTER THEORY OF THE SYMMETRIC GROUP
		A new approach to the character theory of the symmetric group has been developed during the past fifteen years which is in many ways more efficient, more transparent, and more elementary.
		In this approach, to each permutation is assigned a class function of the corresponding symmetric group.
		Problems in character theory can thereby be transferred into a completely different setting and reduced to combinatorial problems on permutations in a natural and uniform way.
	www.icpress.co.uk /mathematics/p369.html (314 words)

	Prisoner's Dilemma
		The above representations of the tragedy of the commons make the simplifying assumptions that the costs and benefits to each player are the same, and that these costs and benefits are independent of the number of players who cooperate.
		The representation differs from the previous one in that the two nodes on each branch within the same division mark simultaneous choices by the two players.
		Selten, Reinhard, "The Chain-Store Paradox," Theory and Decision, 9 (1978): 127-159.
	plato.stanford.edu /entries/prisoner-dilemma (14189 words)

	Hecke algebras and Schur algebras of the symmetric group - Mathas (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		The central aim of this work is to give a concise, but complete, and an elegant, yet quick, treatment of the classification of the simple modules and of the blocks of these two important classes of algebras.
		15 Modular representations of symmetric groups (context) - Littlewood - 1951
		3 the decomposition matrices of the symmetric groups II (context) - James - 1976
	citeseer.lcs.mit.edu /mathas98hecke.html (733 words)

	Graduate Courses, Spring 1997
		The theory of group representations has its roots in the character theory of abelian groups (Gauss, Dirichlet).
		The development of representation theory of finite groups emerged in the early 20th century in the classical work of Frobenius, Schur and Burnside.
		The Symmetric group provides an excellent model for exploring representation theory in general since its irreducible representations can be found using combinatorial techniques accessable to a student with only a knowledge of linear algebra and elementary group theory.
	www.math.temple.edu /grad/spring.courses.html (1118 words)

	GAP 3 Share Package "specht"
		As the (modular) representation theory of these algebras closely resembles that of the (modular) representation theory of the symmetric groups - indeed, the later is a special case of the former - many of the combinatorial tools from the representation theory of the symmetric group are included in this package.
		Specht can be used to compute the decomposition numbers of q-Schur algebras (and the general linear groups), although there is less direct support for these algebras.
		The decomposition matrices for the symmetric groups Sym_n are included for n < 15 and for all primes.
	www-groups.dcs.st-and.ac.uk /~gap/Gap3/Packages3/specht.html (481 words)

	Read This: Briefly Noted, July 2005
		For roughly the last thirty-five years, practitioners of control theory have been aware that complex exponentials play a significant role in the solution of control problems governed by partial differential equations.
		From the control theory side, the concepts of controllability, observability and stabilizability are reviewed in the context of systems governed by partial differential equations.
		While oftentimes this is not done until after probability has been presented, Daniel uses it as motivation for the development of the theory that is needed for formal inference procedures later in the text.
	www.maa.org /reviews/briefly.html (2145 words)

	MA 715 - Representation Theory and the Symmetric Group (Site not responding. Last check: 2007-11-06)
		MA 715, Representation Theory and the Symmetric Group.
		This course serves as an introduction to representation theory.
		TEXTBOOK: Bruce E. Sagan, The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, 2nd Edition, Graduate Texts in Mathematics, Volume 203, Springer-Verlag, 2000.
	www.ms.uky.edu /%7Emath/Research/DM/DM-COURSES/715representation.html (169 words)

	RSNZ: 2004:Wybourne
		He is remembered by physicists for his ground-breaking work on the energy levels of rare-earth ions and applications of Lie groups to the atomic f shell and by mathematicians for his work on group representation theory.
		He investigated the structure of groups and their representations and introduced several areas of esoteric mathematics to physics.
		In particular, he stressed the usefulness to atomic theory of Dudley Littlewood’s theory of plethysms, which is the study of the symmetry of products of objects which themselves possess symmetry.
	www.rsnz.org /directory/yearbooks/2004/wybourne.php (4856 words)

	SPbMS: S.V.Kerov's book (Site not responding. Last check: 2007-11-06)
		Asymptotic representation theory of symmetric groups deals with problems of two types: asymptotic properties of representations of symmetric groups of large order and representations of the limiting object, i.e., the infinite symmetric group.
		This leads to the study of a continuous analog of the notion of Young diagram, and in particular, to a continuous analogue of the hook walk algorithm, which is well known in the combinatorics of finite Young diagrams.
		The book is suitable for graduate students and research mathematicians interested in representation theory and combinatorics.
	www.mathsoc.spb.ru /pers/kerov/book_con.html (295 words)

Try your search on: Qwika (all wikis)