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