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Topic: Gelfand representation

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	Gelfand (Site not responding. Last check: 2007-11-07)
		Gelfand presented his thesis Abstract functions and linear operators in 1935 which contains important results, but is perhaps even more important for the methods that he used, studying functions on normed spaces by applying linear functionals to them and using classical analysis to study the resulting functions.
		Gelfand's work on group representations led him to study integral geometry (a term due to Blaschke) which in turn he was led to by a study of the Radon transform.
		Gelfand's interests were certainly not confined to research despite his incredible record of having published over 500 papers in mathematics, applied mathematics and biology.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Gelfand.html (1035 words)

	Representation Theory (Site not responding. Last check: 2007-11-07)
		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.
		Representation theory is a fundamental tool for studying group symmetry - geometric, analytic, or algebraic - by means of linear algebra.
	math.albany.edu:8000 /math/pers/lenart/teach/repres.html (399 words)

	Research Articles - Julianne Geering Rainbolt (Site not responding. Last check: 2007-11-07)
		The Gelfand-Graev Representation of U(3,q), Journal of Algebra, 188 648-685 (1997).
		Abstract: In this paper we explicitly calculate the irreducible representations of the endomorphism algebra of the Gelfand-Graev representation of the unitary group U(3,q).
		One is the regular representation and one is the usual Gelfand-Graev representation.
	euler.slu.edu /Dept/Faculty/rainbolt/articles.htm (482 words)

	Gelfand representation - Wikipedia, the free encyclopedia
		The spectrum or Gelfand space of a commutative C-algebra A, denoted Â, consists of the set of non-zero complex-valued -homomorphisms on A.
		It also refers to the spectrum σ(x) of an element x of an algebra with unit, that is the set of complex numbers r for which x - r 1 is not invertible in A.
		The Banach-Alaoglu theorem of functional analysis asserts that the unit ball of the dual of a Banach space is weak-* compact.
	en.wikipedia.org /wiki/Gelfand_representation (921 words)

	[No title]
		At any rate, I had known about Gelfand's representation theorem, but had not known that Kolmogorov had done any work of this sort, or that this theorem in particular was due to either of them.
		This result is different from the Gelfand representation theorem that you mention-this result concerns algebras considered without any topology(or norm)-whereas his representation theorem is a result on Banach algebras.
		In historical terms, this result precedes Gelfand's theorem and is the foundation for it-he starts with a general commutative Banach algebra and reconstructs a space from it-thus establishing in what sense that the space to algebra correspondence is surjective, and hence by the aforementioned theorem, bi-unique.
	www.xanga.com /item.aspx?user=m759&tab=weblogs&uid=32033686 (1049 words)

	CPC Licence Alert (Site not responding. Last check: 2007-11-07)
		The inner multiplicity of a particular weight in a given representation, characterised by the highest weight, can be found by counting all distinct Gelfand patterns which belong to the same weight.
		The multiplicity Gamma(0,0,0,0,0)=5 is the representation D(1,1,0,-1,-1) is calculated in.31 s by Honeywell computer and in 20 s by the micro computer.
		The multiplicity Gamma(0,0,0,0,0,0,0,0,0,0)=90 in the representation D(1,1,1,1,0,0,-1,-1,-1,-1) is calculated in 1.6 s by Honeywell computer and 295 s by the micro computer.
	www.cpc.cs.qub.ac.uk /summaries/AATL.html (246 words)

	Israel Gelfand - Wikipedia, the free encyclopedia
		Israel Moiseevich Gelfand (Израиль Моисеевич Гельфанд) (born in 1913) is a prolific mathematician in the field of functional analysis, which he interprets in a broad sense as the mathematics of quantum mechanics.
		He was born into a Jewish family in Okny, Kherson region in Ukraine then part of the Russian Empire.
		and many other results, particularly in the representation theory for the classical groups.
	en.wikipedia.org /wiki/Israel_Moiseevich_Gel'fand (193 words)

	Representations of Matroids in Semimodular Lattices - Borovik, Gelfand, White (ResearchIndex)
		Abstract: We prove equivalence of two definitions of representability of matroids: representation by vector configurations and representation by retraction of buildings of type An.
		Proofs are given in a more general context of representation of matroids in semimodular lattices and Coxeter matroids in chamber systems with group metric.
		Borovik, I. Gelfand and N. White, Representations of matroids in semimodular lattices, submitted.
	citeseer.ist.psu.edu /468315.html (556 words)

	David Vogan's References
		S.I. Gelfand, Weil's representation of the Lie algebra of type G2, and representations of SL3 connected with it, Funct.
		Tsuchikawa, On the representations of SL(3,C), III, Proc.
		Zelevinsky, A p-adic analogue of the Kazhdan-Lusztig conjecture Funct.
	www.math.umd.edu /~jda/vogan_references.html (4364 words)

	Distributional Reciprocity And Generalized Gelfand Pairs (ResearchIndex)
		There has been a great deal of study recently of so-called generalized Gelfand pairs; that is, couples of groups H ae G in which (for the case that G=H has an invariant measure) every space of H-invariant distributions over an irreducible unitary representation of G has dimension at most one.
		It is very well-known that, for any such couple, the quasiregular representation Ind G H 1 is multiplicity-free.
		4 A geometric criterion for Gelfand pairs associated with the..
	citeseer.ist.psu.edu /213334.html (384 words)

	No fixed Vectors
		Our result, however, applies in general, even in cases where the energy representation is known to be reducible.
		We work in the more general context of the ``Gaussian regular representation'' of the Euclidean group of a real separable Hilbert space.
		We show that if a function is invariant under the action of any subgroup of the Euclidean group that has unbounded orbits, then this function must be identically zero.
	math.ucsd.edu /~driver/DRIVER/Preprints/no_fixed_vectors.htm (116 words)

	Hilbert series, Howe duality, and branching rules -- Enright and Willenbring 100 (2): 434 -- Proceedings of the ...
		Suppose that L is a unitarizable highest weight representation occurring in one of the dual pair settings (2.1).
		We have used three separate notations that overlap in the case of finite dimensional representations.
		This is the Hilbert series for the half of the Weil representation generated by a one dimensional representation of k.
	www.pnas.org /cgi/content/full/100/2/434 (1957 words)

	C.J.Mulvey
		The motivating concern behind the research has been to develop the sheaf- and bundle-theoretic foundations to extend the Gelfand representation of C*-algebras from the commutative to the non-commutative case.
		Early work providing the algebraic foundation for this, led to an algebraic generalisation of the Gelfand representation to Gelfand rings, initially of importance in algebraic K-theory and more recently of significance in the algebraic foundations of super-symmetry theory.
		The concept of quantale introduced there allows a Gelfand representation for C-algebras to be obtained, generalising that known in the commutative case, while providing insight into the connections between quantum mechanics and C-algebras.
	www.maths.sussex.ac.uk /Staff/CJM (509 words)

	SSL Minutes (Site not responding. Last check: 2007-11-07)
		We need some representation for TOADs and ASMs that will allow easy cycling through all variations.
		Semi-strict Gelfand Patterns are good >for this application as they are easy to generate.
		Remember, Semi-strict Gelfand Patterns correspond to plane partitions; TOADs and ASMs correspond to monotone triangles.
	www.math.wisc.edu /~propp/SSL/Minutes2001/ssl-minutes-2001-03-06.html (415 words)

	A Bitopological Gelfand Theorem for $C^{}$-Algebras by John Mack (Site not responding. Last check: 2007-11-07)*
		Gelfand, in his delightfully elegant representation theorem, showed that any commutative C
		It is the purpose of this paper to obtain a ``Gelfand type'' representation of an arbitrary (not necessarily commutative) C
		The key idea, here, is to assign two topologies to the base space and then require continuity with respect to both topologies.
	at.yorku.ca /b/a/a/j/16.htm (112 words)

	The First-Order Interacting Space in CSF's (Site not responding. Last check: 2007-11-07)
		It turns out that the simple idea of counting spin flips as excitations, which works so easily for Slater determinants, also works for Gelfand states if the open-shell electrons are at the top of the tableaux.
		Slater's rules make it abundantly clear why this works for Slater determinants, but it is not at all clear why it works for Gelfand states.
		the interacting Gelfand states consist entirely of doubly-excited determinants, whereas the noninteracting ones are expanded as doubly-excited determinants (which give matrix element terms which ``happen'' to cancel) and higher-excited determinants.
	zopyros.ccqc.uga.edu /lec_top/intspc/node3.html (1045 words)

	Abstract Algebra Lab Manual (Site not responding. Last check: 2007-11-07)
		The Gelfand-Graev Representations of U(3,q), Journal of Algebra 188 648-685 (1997).
		The Multiplicity Free Permutation Representations of the Ree Groups and the Suzuki Groups and their Automorphism Groups, Communications in Algebra 31 (3) 1253-1270 (2003), joint work with Jagat Sheth.
		The main goal of this paper is to determine the multiplicity free permutation representations of G and A \leq Aut(G)$ where A is a subgroup containing a copy of G. Teaching Abstract Algebra with GAP, to appear in Proceedings of the 16th Annual International Conference on Technology in Collegiate Mathematics, Pearson Education, Inc., 2005.
	euler.slu.edu /Dept/Faculty/rainbolt/articles.html (508 words)

	Representation Theory (Site not responding. Last check: 2007-11-07)
		A branching theorem describes how an irreducible representation decomposes upon restriction to a subgroup.
		I. Bernstein, I. Gelfand, and S. Gelfand, Structure of representations generated by highest weight vectors, Funct.
		I. Gelfand and M. Cetlin, Finite-dimensional representations of the group of unimodular matrices (Russian), Doklady Akad.
	www.ams.org /ert/2001-005-14/S1088-4165-01-00139-X/home.html (578 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		>>Marshall H Stone, "The Theory of Representation for Boolean Algebras", >>TAMS, v40, (1936), pp 37-111 and "Applications of the Theory of Boolean >>Rings to General Topology" TAMS v41, (1937) pp 385-471.
		In addition to the carefully worked out implicitly categorical concepts of universal solution and adjoint pair, the very idea of constructing a topological representation for anything algebraic first appears here.
		Paul Halmos characterizes Boolean theory as a discretized snapshot of all mathematics taken through the wrong end of a telescope.
	www.math.niu.edu /~rusin/known-math/98/stone (408 words)

	ON NONCOMMUTATIVE GEOMETRY, QUANTUM & SUPER THINGIES.
		While the specific details that would have to be used complicates the concept burdensomely, considerations of geometry from a more abstract point of view make the notion of noncommutative topology more approachable.
		In both commutative and noncommutative cases, it is the duality in the constructions of the theorems which provides the representations of the algebras.
		It is similar in form to angular momentum which can be described both classically and quantally by a Lie algebra so(3) of the special orthogonal group SO(3), but which also acknowledges the Lie algebraic isomorphism of so(3) and su(2), and the ultimate ascendency of su(2).
	graham.main.nc.us /~bhammel/MATH/ncgeom.html (4975 words)

	CV (Site not responding. Last check: 2007-11-07)
		Using Polytopes in the Representation Theory of Lie Algebras, Oberseminar Kombinatorische Geometrie, Technische Universität Berlin, 28 April 2005.
		Integrality of Polytopes from Representation Theory, Otto-von-Guericke-Universitaet Magdeburg, 26 Aug 2004.
		Vertices of Gelfand--Tsetlin Polytopes, Discrete Mathematics and Representation Theory Seminar, University of California, Davis, 14 Nov 2003.
	www.math.ucdavis.edu /~tmcal/CV/CV.html (257 words)

	Amélia Bastos - Home page
		The Gelfand transformation and some of its applications.
		The Gelfand representation theory for commutative Banach algebras.
		Representations of algebras that satisfy a polynomial identity.
	www.math.ist.utl.pt /~abastos/Teaching.html (176 words)

	ZAA 2206 (Site not responding. Last check: 2007-11-07)
		This permits to work out various outstanding nonperiodic homogenization problems that were out of reach till then for lack of an appropriate mathematical framework.
		The classical Gelfand representation theory is one of our main tools and our basic approach is an adaptation of the two-scale convergence method.
		Keywords: Homogenization, homogenization algebra, homogenization structure, Gelfand transformation.
	www.heldermann.de /ZAA/ZAA22/ZAA221/zaa22006.htm (134 words)

	Los Angeles California Business Litigation Attorneys Intellectual Property Employment Contract Lawyers (Site not responding. Last check: 2007-11-07)
		At Gelfand Rappaport and Glaser, our Los Angeles, California business litigation attorneys provide honest and effective legal representation.
		Our legal representation combines the quality of a big law firm with the personal service of a small one.
		For experienced legal representation and unparalleled client service, contact Gelfand Rappaport and Glaser.
	www.grglawyers.com (181 words)

	Amazon.com: Books: C-Algebras and Operator Theory (Site not responding. Last check: 2007-11-07)*
		For Banach algebras with a unit, Gelfand's theorem, giving the non-emptiness of the spectrum, is proven.
		The author also discusses the Gelfand representation, that says essentially that abelian Banach algebras act like continuous functions.
		The representation theory of C*-algebras is considered in chapter 5.
	www.amazon.com /exec/obidos/tg/detail/-/0125113609?v=glance (1326 words)

	Law Offices of Ross Gelfand - Collection/Agency/Attorney
		elcome to the Law Offices of Ross Gelfand, one of the top collection law firms in the nation.
		The growth and reputation for quality legal work of this firm are a direct result of our abilities to effectively represent our clients.
		To help assure the highest level of client representation and proper resolution of their legal problems, members of the firm focus their practice in the commercial and consumer collection area of the law; however, their business backgrounds are diversified enough to handle a wide range of legal issues.
	www.collectionfirm.net (341 words)

	Representation Theory
		A. Beilinson and J. Bernstein, A proof of Jantzen conjectures, I. Gelfand Seminar, Adv.
		J. Bernstein and S. Gelfand, Tensor products of finite- and infinite-dimensional representations of semisimple Lie algebras, Compositio Math.
		D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent.
	www.ams.org /ert/2003-007-26/S1088-4165-03-00189-4/home.html (489 words)

	Math Seminars: Etienne Rassart (Site not responding. Last check: 2007-11-07)
		Kostka numbers and Littlewood-Richardson coefficients appear in the representation theory of complex semisimple Lie algebras of type A, respectively as the multiplicities of weights in irreducible representations, and the multiplicities of irreducible factors in tensor products of irreducibles.
		Despite a number of formulas for them, they are very hard to compute.
		Using a variety of tools from representation theory (Gelfand-Tsetlin diagrams), convex geometry (vector partition functions), symplectic geometry (Duistermaat-Heckman measure) and combinatorics (hyperplane arrangements), we show that, for fixed rank, the weight multiplicities are given by polynomials in the cells of a complex of cones.
	www.math.ias.edu /abstract.php?event=5520 (183 words)

	Gelfand representation (Site not responding. Last check: 2007-11-07)
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		In mathematics, the Gelfand representation in functional analysis allows a complete characterisation of commutative C*-algebrass as algebras of continuous complex-valued functions.
		The Gelfand map on A is defined as follows:
	www.sciencedaily.com /encyclopedia/gelfand_representation (822 words)

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