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Titlebook: Representation Theories and Algebraic Geometry; Abraham Broer,A. Daigneault,Gert Sabidussi Book 1998 Springer Science+Business Media B.V.

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书目名称Representation Theories and Algebraic Geometry
编辑Abraham Broer,A. Daigneault,Gert Sabidussi
视频videohttp://file.papertrans.cn/828/827398/827398.mp4
丛书名称Nato Science Series C:
图书封面Titlebook: Representation Theories and Algebraic Geometry;  Abraham Broer,A. Daigneault,Gert Sabidussi Book 1998 Springer Science+Business Media B.V.
描述The 12 lectures presented in .Representation Theories andAlgebraic. .Geometry. focus on the very rich and powerfulinterplay between algebraic geometry and the representation theoriesof various modern mathematical structures, such as reductive groups,quantum groups, Hecke algebras, restricted Lie algebras, and theircompanions. This interplay has been extensively exploited duringrecent years, resulting in great progress in these representationtheories. Conversely, a great stimulus has been given to thedevelopment of such geometric theories as D-modules, perverse sheafsand equivariant intersection cohomology. .The range of topics covered is wide, from equivariant Chow groups,decomposition classes and Schubert varieties, multiplicity freeactions, convolution algebras, standard monomial theory, and canonicalbases, to annihilators of quantum Verma modules, modularrepresentation theory of Lie algebras and combinatorics ofrepresentation categories of Harish-Chandra modules.
出版日期Book 1998
关键词algebra; algebraic geometry; cohomology; homology; representation theory
版次1
doihttps://doi.org/10.1007/978-94-015-9131-7
isbn_softcover978-90-481-5075-5
isbn_ebook978-94-015-9131-7Series ISSN 1389-2185
issn_series 1389-2185
copyrightSpringer Science+Business Media B.V. 1998
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Some remarks on multiplicity free spaces,presentation. Then we determine all invariant differential operators in terms of a finite reflection group, the little Weyl group, and give a characterization of the spectrum of the Capelli operators. At the end, we reproduce the classification of multiplicity free representations (without proof) annotated with the same basic data.
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Combinatorics of Harish-Chandra modules,the relation of these representation categories with categories of modules over the coinvariant algebra associated to the action of the Weyl group on a Cartan subalgebra. We also discuss conjectural generalizations to the representation theory of real Lie groups.
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Lectures on decomposition classes,we prove the above-mentioned properties. In the last part we study combinatorial invariants associated to decomposition classes and reprove a theorem on the exponents of certain hyperplane arrangements.
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