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Topic: Representations of Lie groups

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	Representation of a Lie group - Wikipedia, the free encyclopedia
		A great deal is known about such representations, a basic tool in their study being the use of the corresponding 'infinitesimal' representations of Lie algebras (indeed in the physics literature the distinction is often elided).
		A representation of a Lie group G on a finite-dimensional complex vector space V is a smooth group homomorphism Ψ:G→Aut(V) from G to the automorphism group of V.
		A representation of a Lie group G on a complex Hilbert space V is a group homomorphism Ψ:G → B(V) from G to B(V), the group of bounded linear operators of V which have a bounded inverse, such that the map G x V → V given by (g,v) → Ψ(g) v is continuous.
	en.wikipedia.org /wiki/Representations_of_Lie_groups/algebras (734 words)

	David Vogan's References
		Dynkin, Semisimple subalgebras of semisimple Lie algebras, Amer.
		Vogan, The algebraic structure of the representations of semisimple Lie groups I, Ann.
		Zelevinsky, A p-adic analogue of the Kazhdan-Lusztig conjecture Funct.
	www.math.umd.edu /~jda/vogan_references.html (4364 words)

	Representations
		Suppose G is a split group of Lie type defined over the field k and r is the least common multiple of the nonzero abelian-group invariants of the coisogeny group of G (see Section Isogeny).
		This happens when r=1, i.e., the group is semisimple and simply connected, or the group is not semisimple but the coisogeny group is torsion free (e.g., the general linear group).
		The highest weight (projective) representation with highest weight v of the group of Lie type G over an extension of its base ring.
	www.math.lsu.edu /magma/text1057.htm (577 words)

	Amazon.ca: Lie Groups: Books: J.J. Duistermaat,J.A.C. Kolk (Site not responding. Last check: 2007-09-05)
		The structure of compact Lie groups is analyzed in terms of the action of the group on itself by conjugation.
		Culminates in the classification of the representations of compact Lie groups and in their relation as sections of holomorphic line bundles over flag manifolds.
		Of particular originality is the theory of orbits for compact groups, an issue with many applications such as the patterns of symmetry breaking in elementary particle physics.
	www.amazon.ca /Lie-Groups-J-J-Duistermaat/dp/3540152938 (456 words)

	(Site not responding. Last check: 2007-09-05)
		In recent years new and important connections have emerged between discrete subgroups of Lie groups, automorphic forms and arithmetic on the one hand, and questions in discrete mathematics, combinatorics, and graph theory on the other.
		A new combinatorial construction of expander graphs was used recently to resolve a group theoretic question on expansion in Cayley graphs.
		People working in one side of the Lie Group/Discrete Math dichotomy are often not aware of the relevance of their work to the other side.
	www.math.ias.edu /liegroups.html (272 words)

	Lie Groups (Site not responding. Last check: 2007-09-05)
		A Lie group (sometimes called a continuous group) is a group on which a structure of differentiable manifold has been defined, such that the two structures are compatible.
		During the 20th century Lie groups and their representations have found connections with many other branches of mathematics e.g.
		Warner, Foundations of Differentiable manifolds and Lie groups, Scott, Foresman and Co., Glenview, IL, 1971.
	www.maths.lth.se /matematiklu/personal/arnem/Liegps.html (270 words)

	Vogan, D.A., Jr.: Unitary Representations of Reductive Lie Groups. (AM-118).
		Vogan, D.A., Jr.: Unitary Representations of Reductive Lie Groups.
		This culminates in the description of all irreducible unitary representation of the general linear groups.
		For other groups, one expects to need a new construction, giving "unipotent representations." The latter half of the book explains the evidence for that expectation and suggests a partial definition of unipotent representations.
	pup.princeton.edu /titles/4161.html (174 words)

	Bien, F.V.: D-Modules and Spherical Representations. (MN-39).
		Hence, it is possible to attach geometric invariants, like the support and the characteristic variety, to representations of Lie groups.
		The problem is then to describe the spherical representations among all irreducible ones, and to compute their multiplicities.
		Using microlocalization of representations, the author derives a criterion for irreducibility.
	pup.princeton.edu /titles/4845.html (190 words)

	2004 Summer Research Conference on Representations of Algebraic Groups, Quantum Groups, and Lie Algebras
		These subjects are very closely related to finite-dimensional representations of affine Hecke algebras, affine quantum groups, Nakajima's quiver varieties, and the structure of Hall algebras.
		In addition, the conference will feature talks on the K-theoretic and geometric approaches towards the understanding of the (nonrestricted) modular representations of Lie algebras and of algebraic groups in positive characteristics.
		Representations of quantum groups at roots of unity and quantum affine algebras
	www.ams.org /meetings/src-benkart.html (190 words)

	On Induced Representations of Lie Algebras, Groups and Coalgebras
		On Induced Representations of Lie Algebras, Groups and Coalgebras
		N.R. Wallach, Induced representations of Lie algebras and a theorem of Borel-Weil, Trans.
		W.H. Wilson, "Induced Representations of Lie Algebras," Ph.D. thesis, University of Sydney, August 1976.
	www.cse.unsw.edu.au /~billw/mathresearch/induced.html (3274 words)

	AMCA: Geometry and smooth representations of reductive Lie groups by Dragan Milicic (Site not responding. Last check: 2007-09-05)
		The standard way of studying representations of reductive Lie groups is to study the corresponding category of Harish-Chandra modules.
		A feature of this approach, which is sometimes unpleasant, is that Harish-Chandra modules do not admit an action of the reductive Lie group G itself (in fact, they are modules for the action of the enveloping algebra of the Lie algebra of the group G and the action of its maximal compact subgroup K).
		Casselman and Wallach defined a category of ``smooth representations of moderate growth and finite length'' of G and constructed a ``completion'' functor from the category of Harish-Chandra modules into this category.
	at.yorku.ca /c/a/e/x/85.htm (366 words)

	640:549 Lie Groups (Site not responding. Last check: 2007-09-05)
		The point of view will be much more analytic than in the Fall 2004 Lie algebra course 640:550, and students with no prior knowledge of Lie algebras should not be at a disadvantage in the Lie groups course.
		Linear Lie groups and their Lie algebras; correspondence between Lie subalgebras and Lie subgroups.
		Integration on manifolds, Lie groups, and homogeneous spaces; Weyl integral formula for compact Lie groups.
	www.math.rutgers.edu /courses/549 (212 words)

	ARCC Workshop: Representations of surface groups (Site not responding. Last check: 2007-09-05)
		The bounded cohomological, the dynamical and the algebro-geometric approach relate the geometry of flag varieties at the boundary of symmetric spaces to the dynamics of surface group actions.
		This has led to a geometric understanding of surface group actions in certain components of the moduli space of representations.
		For split groups, Hitchin found components containing Teichmuller space which are homemorphic to cells, whereas for groups of Hermitian type, there are components of maximal characteristic number (Toledo invariant) comprising certain equivalence classes of discrete Zariski-dense embeddings.
	www.aimath.org /ARCC/workshops/surfacegroups.html (481 words)

	Lie groups and their representations (Site not responding. Last check: 2007-09-05)
		"Mikio Ise and Masaru Takeuchi, "Lie groups I" (and II), Translations of mathematical monographs volume 85.
		Duistermaat and J. Kolk, Lie Groups, Springer, 2000.
		C, structure and classification of complex semi-simple Lie algebras, complex Lie groups and their representations.
	www.ma.huji.ac.il /~karshon/teaching/2000-01/Lie (171 words)

	[No title] (Site not responding. Last check: 2007-09-05)
		Representations of Lie groups, convolution algebras, and Lie algebras
		Representations of compact groups on eigenspaces of Laplace operators
		Nilpotent Lie algebras and Lie algebras with dilations
	www.math.unc.edu /Faculty/met/nharm.html (127 words)

	The Math Forum - Math Library - Topo./Lie Groups
		Thus Lie groups and other topological groups lie at the convergence of the different areas of pure mathematics.
		An electronic journal for speedy publication of information in the following areas: Lie algebras, Lie groups, algebraic groups, and related types of topological groups such as locally compact and compact groups.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /library/topics/group_topol (490 words)

	Langlands (print-only)
		He submitted his thesis Semi-groups and representations of Lie groups to Yale in 1960 and received the degree of Ph.D. Langlands wrote:-
		It nevertheless had the good fortune to be taken seriously by Derek Robinson, who incorporated some of the results into his book on Elliptic Operators and Lie Groups.
		extraordinary vision that has brought the theory of group representations into a revolutionary new relationship with the theory of automorphic forms and number theory.
	www-groups.dcs.st-and.ac.uk /history/Printonly/Langlands.html (825 words)

	Topics in Representation Theory of Lie Groups and Lie Algebras (Site not responding. Last check: 2007-09-05)
		Topics in Representation Theory of Lie Groups and Lie Algebras
		: Our goal is to introduce students to the finite dimensional representations of compact Lie groups and their Lie algebras.
		The course will cover most of the fundamental results and techniques, including the Weyl character formula, in forms suitable for applications to physics, geometry, and topology.
	www.math.usu.edu /~dariusz/syllabus7310S2004.html (91 words)

	Math 522. Lie Groups and Lie Algebras I
		(1) A summary of the theory of finite group representations, including the symmetric group.
		(3) Lie algebras: As the tangent space at the identity to the Lie group, and also the definition as abstract objects.
		(4) Representations of Lie groups and Lie algebras: Definition and some examples.
	www.math.uiuc.edu /Bourbaki/Syllabi/syl522.html (74 words)

	Representation Theory
		This course will cover various aspects of the representation theory of Lie groups.
		aspects of representation theory, as well as their relationship to quantum mechanics.
		Lie Groups, Lie Algebras and the Exponential Map
	www.math.columbia.edu /~woit/repthy.html (96 words)

	Representations of Nilpotent Lie Groups and their Applications - Cambridge University Press (Site not responding. Last check: 2007-09-05)
		Representations of Nilpotent Lie Groups and their Applications - Cambridge University Press
		Representations of Nilpotent Lie Groups and their Applications
		Representations of Nilpotent Lie Groups and their Applications (Hardback)
	www.cambridge.org /catalogue/email.asp?isbn=052136034X (143 words)

	DC MetaData for: On the Representations of Lie Groups and Lie Algebras in Rigged Hilbert Spaces
		DC MetaData for: On the Representations of Lie Groups and Lie Algebras in Rigged Hilbert Spaces
		On the Representations of Lie Groups and Lie Algebras in Rigged Hilbert Spaces
		22E60 Lie algebras of Lie groups, {For the algebraic theory of Lie algebras, See 17Bxx}
	www.esi.ac.at /Preprint-shadows/esi994.html (98 words)

	Robert Langlands' work - semi-groups and representation theory (Site not responding. Last check: 2007-09-05)
		This was submitted for a Ph.D. thesis in mathematics at Yale University.
		There are two, related parts to this thesis: one on representations of Lie semi-groups and one on operators associated to representations of Lie groups.
		Examining again, after forty years, the verification of the basic estimates of the second part, I found a large number of misprints, so that it would have been difficult if not impossible to follow my arguments line by line.
	www.sunsite.ubc.ca /DigitalMathArchive/Langlands/thesis.html (217 words)

	Analytic continuation of local representations of Lie groups., Palle E. T. Jorgensen (Site not responding. Last check: 2007-09-05)
		Analytic continuation of local representations of Lie groups., Palle E. Jorgensen
		Analytic continuation of local representations of Lie groups.
		[18] R. Penney, Harmonically induced representations on nilpotent Lie groups and automorphic forms on nilmanifolds, Trans.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.pjm/1102700084 (325 words)

	Atlas of Lie Groups and Representations (Site not responding. Last check: 2007-09-05)
		This is a project to make available information about representations semi-simple Lie groups over real and p-adic fields.
		Of particular importance is the problem of the unitary dual: classifying all of the irreducible unitary representations of a given Lie group.
		We are also planning to make information about Lie groups and representation theory, in particular unitary representations, available to the general mathematical public.
	atlas.math.umd.edu (229 words)

	AMCA: Complex Geometry and Representations of Lie Groups by Joseph A. Wolf (Site not responding. Last check: 2007-09-05)
		AMCA: Complex Geometry and Representations of Lie Groups by Joseph A. Wolf
		Let G be a real semisimple Lie group.
		Let [^G] denote its unitary dual, the set of (equivalence classes of) irreducible unitary representations of G. In general [^G] is not known, but the subset involved in the Plancherel formula for G is pretty well understood.
	at.yorku.ca /c/a/d/q/38.htm (255 words)

	Publications
		Signature quantization, representations of compact Lie groups, and a q-analogue of the Kostant partition function.
		(Une version étendue de l'article Signature quantization and representations of compact Lie groups, avec Victor Guillemin).
		Signature quantization and representations of compact Lie groups.
	www.math.cornell.edu /~rassart/publications.html (190 words)

	Semisimple Lie groups books, find the lowest prices (Site not responding. Last check: 2007-09-05)
		Harmonic Analysis and Representations of Semi-Simple Lie Groups : Lectures Given at the NATO Advanced Study Institute on Representations of Lie Group
		Cahen, Joseph Albert Wolf, NATO Advanced Study Institute on Representations of Lie Groups and Har, M.
		An Introduction to Harmonic Analysis on Semisimple Lie Groups
	www.allbookstores.com /Semisimple_Lie_Groups_st.html (194 words)

	Publisher description for Library of Congress control number 90008776
		Publisher description for D-modules and spherical representations / by Frâedâeric V. Bien.
		Bibliographic record and links to related information available from the Library of Congress catalog
		Library of Congress subject headings for this publication: Differentiable manifolds, D-modules, Representations of groups, Lie groups
	www.loc.gov /catdir/description/prin031/90008776.html (237 words)

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