Memoirs of the American Mathematical Society 2002; 95 pp; softcover Volume: 157 ISBN10: 0821828916 ISBN13: 9780821828915 List Price: US$56 Individual Members: US$33.60 Institutional Members: US$44.80 Order Code: MEMO/157/749
 In this paper we prove Lusztig's conjecture on based ring for an affine Weyl group of type \(\tilde A_{n1}\). Readership 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 \(\widetilde{A}_{n1}\)
 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
