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Hecke algebras of finite type are cellular

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Abstract

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 A n and B n .

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  1. Department of Mathematical Sciences, King’s College, Aberdeen University, Meston Building, AB24 3UE, Aberdeen, Scotland, UK

    Meinolf Geck

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Geck, M. Hecke algebras of finite type are cellular. Invent. math. 169, 501–517 (2007). https://doi.org/10.1007/s00222-007-0053-2

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