In 1985, Lusztig defined a function for any Coxeter group by using the Kazhdan-Lusztig basis of the Hecke algebra of . The -function has important connections with the cell representation theory of and its Hecke algebra, but is usually difficult to compute directly. However, it is known that an element has -value 1 if and only it it is a non-identity element with a unique reduced word, and that contains finitely many elements of -value 1 if and only the Coxeter diagram of satisfies certain conditions. In this talk, we describe a similar classification, in terms of Coxeter diagrams, of all Coxeter groups with finitely many elements of -value 2. We will show that elements of -value 2 are fully commutative in the sense of Stembridge, and our main tools for the classification include Viennot's heaps and certain so-called star operations on Coxeter groups. (Joint work with Richard Green.)
Classification of a(2)-finite Coxeter groups
Sep. 17, 2019 4pm (MATH 350)
Topology
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