Contemporary Mathematics 1993; 200 pp; softcover Volume: 153 ISBN10: 0821851616 ISBN13: 9780821851616 List Price: US$50 Member Price: US$40 Order Code: CONM/153
 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 avenueswith 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 KacMoody 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 KacMoody 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
