## Structure of a Hecke algebra quotient

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- by C. Kenneth Fan
- J. Amer. Math. Soc.
**10**(1997), 139-167 - DOI: https://doi.org/10.1090/S0894-0347-97-00222-1
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## Abstract:

Let $W$ be a Coxeter group with Coxeter graph $\gamma$. Let $\mathcal {H}$ be the associated Hecke algebra. We define a certain ideal $\mathcal {I}$ in $\mathcal {H}$ and study the quotient algebra $\bar {\mathcal {H}} = \mathcal {H}/\mathcal {I}$. 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 $H$.## References

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## Bibliographic Information

**C. Kenneth Fan**- Email: ckfan@math.harvard.edu
- Received by editor(s): May 14, 1996
- Additional Notes: Supported in part by a National Science Foundation postdoctoral fellowship.
- © Copyright 1997 American Mathematical Society
- 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

Dedicated: Dedicated to my teacher, George Lusztig, on his fiftieth birthday