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Structure of a Hecke algebra quotient

Author: C. Kenneth Fan
Journal: J. Amer. Math. Soc. 10 (1997), 139-167
MSC (1991): Primary 16G30, 05E99; Secondary 16D70, 20F55
MathSciNet review: 1396894
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Abstract: Let $W$ be a Coxeter group with Coxeter graph ${\Gamma } $. Let $\cal H$ be the associated Hecke algebra. We define a certain ideal ${\cal I}$ in $\cal H$ and study the quotient algebra ${\bar {\cal H}} = {\cal H}/{\cal I}$. We show that when ${\Gamma } $ is one of the infinite series of graphs of type $E$, the quotient is semi-simple. We examine the cell structures of these algebras and construct their irreducible representations. We discuss the case where ${\Gamma } $ is of type $B$, $F$, or $H$.

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Additional Information

C. Kenneth Fan

Keywords: Iwahori-Hecke algebra, Temperley-Lieb algebra, Coxeter group, cell theory, semi-simple algebra
Received by editor(s): May 14, 1996
Additional Notes: Supported in part by a National Science Foundation postdoctoral fellowship.
Dedicated: Dedicated to my teacher, George Lusztig, on his fiftieth birthday
Article copyright: © Copyright 1997 American Mathematical Society