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University of Sydney Algebra Seminar

Bob Howlett

Friday 4 November, 3-4pm, Place: Carslaw 451

W-graph representations of reflection groups and Iwahori–Hecke algebras

A W-graph is essentially a basis of a module for a reflection group W or its associated Hecke algebra H. The basis elements are represented as vertices of the graph, and labels on the vertices and edges describe the action of the generators of the group or algebra on the basis elements. It is a theorem that in the completely reducible case every representation of W or H corresponds to a W-graph. For the exceptional types W-graphs have been explicitly computed for all the irreducible representations, and in type A there is an algorithm for computing a W-graph for any irreducible. But no such algorithm is known for type B.