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Journal of the American Mathematical Society

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ISSN 1088-6834 (online) ISSN 0894-0347 (print)

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Structure of a Hecke algebra quotient
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by C. Kenneth Fan
J. Amer. Math. Soc. 10 (1997), 139-167


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 $H$.
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Bibliographic Information
  • C. Kenneth Fan
  • Email:
  • 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
  • © Copyright 1997 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 10 (1997), 139-167
  • MSC (1991): Primary 16G30, 05E99; Secondary 16D70, 20F55
  • DOI:
  • MathSciNet review: 1396894