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Algebraic Groups and Their Generalizations
Edited by: William J. Haboush and Brian J. Parshall

Proceedings of Symposia in Pure Mathematics
1994; 798 pp; hardcover
Volume: 56
ISBN-10: 0-8218-1497-4
ISBN-13: 978-0-8218-1497-0
List Price: US$169
Member Price: US$135.20
Order Code: PSPUM/56
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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 infinite-dimensional 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 infinite-dimensional 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.


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 Kazhdan-Lusztig theory and related topics
  • R. Dipper -- Green theory for Hecke algebras and Harish-Chandra 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 subgroup-schemes
  • 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. Moser-Jauslin -- 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 infinite-dimensional 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 algebras--A 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 finite-dimensional Lie algebras
  • A. G. Helminck and G. F. Helminck -- Holomorphic line bundles over Hilbert flag varieties
  • L. Natarajan, E. Rodríguez-Carrington, and J. A. Wolf -- New classes of infinite-dimensional Lie groups
  • G. Rousseau -- On forms of Kac-Moody algebras
  • A. A. Voronov -- Semi-infinite cohomology of Lie algebras
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