Abstract
We consider simple modules for a Hecke algebra with a parameter of quantum characteristic e. Equivalently, we consider simple modules D λ, labelled by e-restricted partitions λ of n, for a cyclotomic KLR algebra \( {R}_n^{\varLambda_0} \) over a field of characteristic p ≥ 0, with mild restrictions on p. If all parts of λ are at most 2, we identify a set DStde, p (λ) of standard λ-tableaux, which is defined combinatorially and naturally labels a basis of D λ. In particular, we prove that the q-character of D λ can be described in terms of DStde, p (λ). We show that a certain natural approach to constructing a basis of an arbitrary D λ does not work in general, giving a counterexample to a conjecture of Mathas.
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We record with deep sadness the passing of Anton Evseev on 21st February 2017
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DE BOECK, M., EVSEEV, A., LYLE, S. et al. ON BASES OF SOME SIMPLE MODULES OF SYMMETRIC GROUPS AND HECKE ALGEBRAS. Transformation Groups 23, 631–669 (2018). https://doi.org/10.1007/s00031-017-9444-7
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DOI: https://doi.org/10.1007/s00031-017-9444-7