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The Based Ring of Two-Sided Cells of Affine Weyl Groups of Type \(\widetilde{A}_{n-1}\)
Nanhua Xi, Chinese Academy of Sciences, Institute of Mathematics, Beijing, China

Memoirs of the American Mathematical Society
2002; 95 pp; softcover
Volume: 157
ISBN-10: 0-8218-2891-6
ISBN-13: 978-0-8218-2891-5
List Price: US$59
Individual Members: US$35.40
Institutional Members: US$47.20
Order Code: MEMO/157/749
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In this paper we prove Lusztig's conjecture on based ring for an affine Weyl group of type \(\tilde A_{n-1}\).


Graduate students and research mathematiciains interested in group theory and generalizations, category theory, and homological algebra.

Table of Contents

  • Cells in affine Weyl groups
  • Type \(\widetilde{A}_{n-1}\)
  • Canonical left cells
  • The group \(F_\lambda\) and its representation
  • A bijection between \(\Gamma_\lambda\cap\Gamma^{-1}_\lambda\) and Irr \(F_\lambda\)
  • A factorization formula in \(J_{\Gamma_\lambda\cap\Gamma^{-1}_\lambda}\)
  • a multiplication formula in \(J_{\Gamma_\lambda\cap\Gamma^{-1}_\lambda}\)
  • The based rings \(J_{\Gamma_\lambda\cap\Gamma^{-1}_\lambda}\) and \(J_{\mathbf{c}}\)
  • Bibliography
  • Index
  • Notation
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