Proceedings of Symposia in Pure Mathematics 1994; 798 pp; hardcover Volume: 56 ISBN10: 0821814974 ISBN13: 9780821814970 List Price: US$162 Member Price: US$129.60 Order Code: PSPUM/56
 These volumes contain papers based on lectures presented at the conference, "Algebraic Groups and Their Generalizations", held at Pennsylvania State University in July 1991. An outgrowth of the remarkable proliferation of Lie theory in the last fifteen years, this conference reflected both the diversification of technique in the classical theory and the beginnings of the study of new objects. These new objects include quantum groups and vertex operator algebras, as well as various kinds of infinitedimensional groups and algebras inspired by new work in mathematical physics and quantum field theory. The first volume focuses on classical methods, while the second centers on quantum and infinitedimensional methods. Each section begins with expositions and then turns to new results. This collection provides readers with an excellent introduction to these astonishing new mathematical worlds. Readership Researchers in algebraic geometry, representation theory, and Lie theory; research mathematicians in other areas interested in finding out more about new developments in this area. Table of Contents Part 1. Classical methods  C. Chevalley  Sur les decompositions cellulaires des espaces \(G/B\)
 A. Borel  Introduction to middle intersection cohomology and perverse sheaves
 J. B. Carrell  The Bruhat graph of a Coxeter group, a conjecture of Deodhar, and rational smoothness of Schubert varieties
 E. Cline, B. Parshall, and L. Scott  Simulating perverse sheaves in modular representation theory
 V. Deodhar  A brief survey of KazhdanLusztig theory and related topics
 R. Dipper  Green theory for Hecke algebras and HarishChandra philosophy
 M. Schaps  Liftable deformations and Hecke algebras
 E. A. Siegel  A Hecke algebra of the symmetric group
 B. Srinivasan  Character sheaves: Applications to finite groups
 R. J. Bremigan  Real algebraic quotients
 M. Brion and S. P. Inamdar  Frobenius splitting of spherical varieties
 R. Dąbrowski  Generalized Kloosterman sums
 A. G. Helminck  Symmetric \(k\)varieties
 A. R. Magid  Identities for prounipotent groups
 C. Wenzel  On the structure of nonreduced parabolic subgroupschemes
 A. J. Coleman  Weight modules without highest weight
 J. E. Humphreys  Extremal composition factors for groups of Lie type
 K. Kazuhiko  Relative invariants of the polynomial rings over the finite and tame type quivers
 B. Broer  Hilbert series for modules of covariants
 R. E. Howe  The first fundamental theorem of invariant theory and spherical subgroups
 M. Masuda and T. Petrie  Algebraic families of \(O(2)\)actions on affine space \(\mathbf C^4\)
 L. MoserJauslin  Algebraic equivariant vector bundles and the linearity problem
 G. F. Seelinger  Equivariant matrix valued functions
 D. L. Wehlau  Constructive invariant theory
Part 2. Quantum and infinitedimensional methods  H. H. Andersen  Finite dimensional representations of quantum groups
 P. Cartier  An introduction to quantum groups
 B. Enriquez  Examples of compact matrix pseudogroups arising from Drinfel'd's twisting operation
 T. Hayashi  Face algebras and their Drinfeld doubles
 G. Letzter  Representation theory for quantized enveloping algebras
 Z. Lin  Rational representations of Hopf algebras
 J. Paradowski  Filtrations of modules over the quantum algebra
 A. Sudbery  Quantum groups as invariance groups
 M. Takeuchi  The quantum hyperalgebra of \(SL_q(2)\)
 J. Du  IC bases and quantum linear groups
 V. Lakshmibai  Bases for quantum Demazure modules. II
 G. Lusztig  Problems on canonical bases
 M. M. Kapranov and V. A. Voevodsky  \(2\)categories and Zamolodchikov tetrahedra equations
 C. Dong and J. Lepowsky  Abelian intertwining algebrasA generalization of vertex operator algebras
 C. Dong, G. Mason, and Y. Zhu  Discrete series of the Virasoro algebra and the moonshine module
 A. J. Feingold  Constructions of vertex operator algebras
 Y.Z. Huang  Binary trees and finitedimensional Lie algebras
 A. G. Helminck and G. F. Helminck  Holomorphic line bundles over Hilbert flag varieties
 L. Natarajan, E. RodríguezCarrington, and J. A. Wolf  New classes of infinitedimensional Lie groups
 G. Rousseau  On forms of KacMoody algebras
 A. A. Voronov  Semiinfinite cohomology of Lie algebras
