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Titlebook: New Developments in Lie Theory and Their Applications; Juan Tirao,Nolan R. Wallach Book 1992 Birkhäuser Boston 1992 algebra.lie group.repr

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书目名称New Developments in Lie Theory and Their Applications
编辑Juan Tirao,Nolan R. Wallach
视频video
丛书名称Progress in Mathematics
图书封面Titlebook: New Developments in Lie Theory and Their Applications;  Juan Tirao,Nolan R. Wallach Book 1992 Birkhäuser Boston 1992 algebra.lie group.repr
描述Representation theory, and more generally Lie theory, has played a very important role in many of the recent developments of mathematics and in the interaction of mathematics with physics. In August-September 1989, a workshop (Third Workshop on Representation Theory of Lie Groups and its Applications) was held in the environs of C6rdoba, Argentina to present expositions of important recent developments in the field that would be accessible to graduate students and researchers in related fields. This volume contains articles that are edited versions of the lectures (and short courses) given at the workshop. Within representation theory, one of the main open problems is to determine the unitary dual of a real reductive group. Although this prob­ lem is as yet unsolved, the recent work of Barbasch, Vogan, Arthur as well as others has shed new light on the structure of the problem. The article of D. Vogan presents an exposition of some aspects of this prob­ lem, emphasizing an extension of the orbit method of Kostant, Kirillov. Several examples are given that explain why the orbit method should be extended and how this extension should be implemented.
出版日期Book 1992
关键词algebra; lie group; representation theory
版次1
doihttps://doi.org/10.1007/978-1-4612-2978-0
isbn_softcover978-1-4612-7743-9
isbn_ebook978-1-4612-2978-0Series ISSN 0743-1643 Series E-ISSN 2296-505X
issn_series 0743-1643
copyrightBirkhäuser Boston 1992
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On Spherical Modules,Let . be a group, . a finite dimensional complex vector space and . : . → .(.) a representation. Let us denote by . the ring of all polynomial functions on .; clearly . acts on .(.). The main problem of the classical invariant theory can be phrased as follows: To find explicitly all the .-invariant polynomial functions on ..
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Generalized Weil Representations for SL(n,k), n odd, k a Finite Field,Generalized Weil representations for the group . = SL(.), . a finite field, are constructed by contraction of a suitable complex .-vector bundle with the help of an appropriate connection. This extends a previous construction by the authors for the case where . is even, obtained with the help of “Grassmann-Heisenberg” groups.
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