Hecke algebras of finite type are cellular

By Meinolf Geck. 2006

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Let $\mathcal{H}$ be the one-parameter Hecke algebra associated to a finite Weyl group W, defined over a ground ring in which “bad” primes for W are invertible. Using deep properties of the Kazhdan–Lusztig basis of $\mathcal{H}$ and Lusztig’s a-function, we show that $\mathcal{H}$ has a natural cellular structure in the sense of Graham and Lehrer. Thus, we obtain a general theory of “Specht modules” for Hecke algebras of finite type. Previously, a general cellular structure was only known to exist in types An and Bn.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/50634da3bb946a7c6f095e3885c1eb3ded416cf1