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

DOI:
https://doi.org/10.1090/S0894-0347-97-00222-1

MathSciNet review:
1396894

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Abstract: Let be a Coxeter group with Coxeter graph . Let be the associated Hecke algebra. We define a certain ideal in and study the quotient algebra . We show that when is one of the infinite series of graphs of type , the quotient is semi-simple. We examine the cell structures of these algebras and construct their irreducible representations. We discuss the case where is of type , , or .

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Additional Information

**C. Kenneth Fan**

Email:
ckfan@math.harvard.edu

DOI:
https://doi.org/10.1090/S0894-0347-97-00222-1

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