# Mathematics Colloquia and Seminars

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### Hecke algebra deformations of Coxeter group actions

**Algebra & Discrete Mathematics**

Speaker: | Eric Rains, UC Davis |

Location: | 693 Kerr |

Start time: | Fri, Nov 7 2003, 2:10PM |

Given a Coxeter group (say, for instance, the symmetric group), there is a natural way to deform its group algebra to an algebra called the Hecke algebra. While the representation theory of the Coxeter group carries over to the Hecke algebra, much of the other structure does not. I will discuss some work in progress with M. Vazirani on the following question: When does a permutation action of a Coxeter group admit a natural deformation to a Hecke algebra representation? Even within the class of deformations we consider, the answer turns out to be remarkably subtle: for instance, the action of the symmetric group on perfect matchings admits two distinct deformations. In addition, many of our deformations, although constructed in purely Coxeter theoretic terms, turn out to have natural interpretations in finite geometry.