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Linear Algebraic Groups and Their Representations
Edited by: Richard S. Elman, Murray M. Schacher, and V. S. Varadarajan
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Contemporary Mathematics
1993; 200 pp; softcover
Volume: 153
ISBN-10: 0-8218-5161-6
ISBN-13: 978-0-8218-5161-6
List Price: US$50
Member Price: US$40
Order Code: CONM/153
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This book contains the proceedings of the Conference on Linear Algebraic Groups and Their Representations, held at UCLA in March 1992. The central theme is the fundamental nature of this subject and its interaction with a wide variety of active areas in mathematics and physics. Linear algebraic groups and their representations interface with a broad range of areas through diverse avenues--with algebraic geometry through moduli spaces, with classical invariant theory through group actions on polynomial rings, with enumerative and combinatorial geometry through flag manifolds, and with theoretical physics through Kac-Moody algebras and quantum groups. Collected here are both surveys and original contributions by eminent specialists, reflecting current developments in the subject. This book is one of the few available sources that brings together such a wide variety of themes under a single unifying perspective.

Readership

Specialists and or students concentrating in algebraic geometry, algebraic groups, or invariant theory.

Table of Contents

  • W. Feit -- Extending Steinberg characters
  • I. Grojnowski and G. Lusztig -- A comparison of bases of quantized enveloping algebras
  • R. M. Guralnick and A. Weiss -- Transitive permutation lattices in the same genus and embeddings of groups
  • W. Haboush and N. Lauritzen -- Varieties of unseparated flags
  • V. Lakshmibai -- Bases for Demazure modules for symmetrizable Kac-Moody algebras
  • K. C. Misra -- Representations of quantum affine Lie algebras and crystal bases
  • M. S. Raghunathan and T. N. Venkataramana -- The first Betti number of arithmetic groups and the congruence subgroup problem
  • R. W. Richardson and T. A. Springer -- Combinatorics and geometry of \(K\)-orbits on the flag manifold
  • G. E. Röhrle -- On extraspecial parabolic subgroups
  • G. M. Seitz -- Bounds for dimensions of weight spaces of maximal tori
  • C. S. Seshadri -- Vector bundles on curves
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