Recently I showed that Hecke algebras of finite type are cellular
in the sense of Graham-Lehrer. This leads to a natural generalisation of the
theory of Specht modules to Hecke algebras of any (finite) type. In this
framework, we can also formulate a general version of James conjecture, and
we obtain a straightforward algorithm for verifying it. In joint work
with Juergen
Mueller, we used this approach to prove James' conjecture for Hecke algebras
of exceptional type.

Lecture #12685

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