Representation Theories and Algebraic Geometry

Representation Theories and Algebraic Geometry

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The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology.
The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.
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Product details

  • Hardback | 444 pages
  • 210 x 297 x 25.4mm | 1,840g
  • Dordrecht, Netherlands
  • English
  • 1998 ed.
  • XXII, 444 p.
  • 0792351932
  • 9780792351931

Table of contents

Preface. Equivariant Cohomology and Equivariant Intersection Theory; M. Brion. Lectures on Decomposition Classes; A. Broer. Instantons and Kahler Geometry of Nilpotent Orbits; R. Brylinski. Geometric Methods in the Representation Theory of Hecke Algebras and Quantum Groups; V. Ginzburg. Representations of Lie Algebras in Prime Characteristics; J.C. Jantzen. Sur l'annulateur d'un module de Verma; A. Joseph. Some Remarks on Multiplicity Free Spaces; F. Knop. Standard Monomial Theory and Applications; V. Lakshmibai, et al. Canonical Bases and Hall Algebras; G. Lusztig. Combinatorics of Harish-Chandra Modules; W. Soergel. Schubert Varieties and Generalizations; T.A. Springer. Index.
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