In this paper we prove Lusztig's conjecture on based ring for an affine Weyl group of type \(\tilde A_{n-1}\).

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 \(\widetilde{A}_{n-1}\)
• 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