Representations of Algebraic Groups, Quantum Groups, and Lie Algebras

Representations of Algebraic Groups, Quantum Groups, and Lie Algebras

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The book contains several well-written, accessible survey papers in many interrelated areas of current research. These areas cover various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie super algebras. Geometric methods have been instrumental in representation theory, and these proceedings include surveys on geometric as well as combinatorial constructions of the crystal basis for representations of quantum groups. Humphreys' paper outlines intricate connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic, left cells in two sided cells of affine Weyl groups, and the geometry of the nilpotent orbits. All these papers provide the reader with a broad picture of the interaction of many different research areas and should be helpful to those who want to have a glimpse of current research involving representation theory.
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Product details

  • Paperback | 254 pages
  • 177.8 x 254 x 19.05mm | 476.27g
  • Providence, United States
  • English
  • illustrated Edition
  • 0821839241
  • 9780821839249

Table of contents

Extensions for finite groups of Lie type II: Filtering the truncated induction functor by C. P. Bendel, D. K. Nakano, and C. Pillen Algebras, representations and their derived categories over finite fields by B. Deng and J. Du On localization of $\bar D$-modules by Y. Hashimoto, M. Kaneda, and D. Rumynin Representations of reduced enveloping algebras and cells in the affine Weyl group by J. E. Humphreys Nakajima's monomials and crystal bases by S.-J. Kang, J.-A. Kim, and D.-U. Shin A new Lie bialgebra structure on $sl(2,1)$ by G. Karaali The Steinberg tensor product theorem for $GL(m/n)$ by J. Kujawa Cyclotomic $q$-Schur algebras and Schur-Weyl duality by Z. Lin and H. Rui Geometric crystals and affine crystals by T. Nakashima Self-extensions for finite symplectic groups via algebraic groups by C. Pillen Classification of finite dimensional simple Lie algebras in prime characteristics by A. Premet and H. Strade From quantum groups to unitary modular tensor categories by E. C. Rowell A trip from representations of the Kronecker quiver to canonical bases of quantum affine algebras by J. Xiao and G. Zhang.
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