Results 251 to 260 of about 2,757,536 (270)

Representations of Lie Groups and Supergroups

Oberwolfach Reports, 2013
The workshop focussed on recent developments in the representation theory of group objects in several categories, mostly finite and infinite dimensional smooth manifolds and supermanifolds. The talks covered a broad range of topics, with a certain emphasis on benchmark problems and examples such as branching, limit behavior, and dual pairs.
Tudor S. Ratiu, Karl-Hermann Neeb, Toshiyuki Kobayashi, Joachim Hilgert   +3 more
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Lie Groups, Lie Algebras, and Representations

2003
An important concept in physics is that of symmetry, whether it be rotational symmetry for many physical systems or Lorentz symmetry in relativistic systems. In many cases, the group of symmetries of a system is a continuous group, that is, a group that is parameterized by one or more real parameters.
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Representation of Lie Groups and Lie Algebras

2013
The representation of Lie groups is closely related to the representation of their Lie algebras, and we shall discuss them later in this chapter. In the case of compact groups, however, there is a well developed representation theory, which we shall consider in the first section.
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Introduction to Lie Groups and Their Representations

2012
This Chapter consists of a brief survey of the most important concepts of group theory, having in mind the applications to physical problems. After a collection of general notions which apply both to finite and infinite groups,we shall consider the properties of the Lie groups and their representations.We shall avoid mathematical rigour and ...
Giovanni Costa, Gianluigi Fogli
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Representations of graded Lie groups

Journal of Mathematical Physics, 1983
In this paper we establish the existence of a faithful matrix representation of finite type for every connected simply connected graded Lie group. We also show the 1-1 correspondence between finite-dimensional representations of a graded Lie algebra and the representations of finite type of the corresponding connected simply connected graded Lie group.
K. C. Tripathy, B. R. Sitaram
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Representations of simple lie groups

Reports on Mathematical Physics, 1993
Abstract We prove the equivalence of the following conditions for a compact simple Lie group G : (1) G admits complex representations; (2) the center of G contains elements of order higher than two; (3) G has Casimir invariants of odd order; (4) the expansion of G in real homology spheres H ∗ ;(G; R ) = H ∗ ;(S 3 × S
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Representations of Compact Lie Groups [PDF]

, 1997
Compact Lie groups are ‘perfect’ entities in modern mathematics because: (a) They are differentiable (and even analytical) manifolds of finite dimension and therefore can be analysed with the help of the most powerful tool of mathematics: ordinary and partial differential operators (equations); (b) Denoting by £(G) or L(G) = T e (G ...
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Representations of Semisimple Lie Groups

2010
The purpose of these lectures is to give an elementary introduction to some basic topics in the theory of representations of semisimple Lie groups. Within harmonic analysis I have limited myself to a special topic which is now fairly well-developed, namely Fourier analysis of spherical functions.
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Representation Theory of Lie Groups

1980
Lie groups and their representations occupy an important place in mathematics with applications in such diverse fields as differential geometry, number theory, differential equations and physics. In 1977 a symposium was held in Oxford to introduce this rapidly developing and expanding subject to non-specialists. This volume contains the lectures of ten
Michael Atiyah, G. Lustztig, Bertram Kostant, Raoul Bott, D. Kazhdan, Sigurdur Helgason   +5 more
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Representations of Groups of Lie Type

2019
The final chapter is the representation theory of groups of Lie type, both in defining and non-defining characteristics. The first section deals with defining characteristic representations, introducing highest weight modules, Weyl modules, and building up to the Lusztig conjecture, with a diversion into Ext1 between simple modules for the algebraic ...
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