Decomposition Matrices for the Generic Hecke Algebras on 3 Strands in Characteristic 0

Chavli, Eirini

doi:10.1007/s10468-019-09867-7

Cited by 2 publications

(1 citation statement)

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“…Before we finish this section, we should mention here that there is another work on decomposition matrices of exceptional complex reflection groups, Chavli's paper [Cha3] on the generic Hecke algebras of G 4 , G 8 and A symmetrising trace τ was defined in [CPA2] on K(q)Y(d, l, n); this map satisfies τ (b) = δ 1b for all b in a certain basis of Y(d, l, n). The map τ coincides with the canonical symmetrising trace on H q n for d = 1 and with the symmetrising trace defined on the Yokonuma-Hecke algebra of type A in [CPA1] for l = 1.…”

Section: Defect In Cyclotomic Hecke Algebras Of Exceptional Groupsmentioning

confidence: 99%

Defect in cyclotomic Hecke algebras

Chlouveraki,

Jacon

2021

Preprint

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The complexity of a block of a symmetric algebra can be measured by the notion of defect, a numerical datum associated to each of the simple modules contained in the block. Geck showed that the defect is a block invariant for Iwahori-Hecke algebras of finite Coxeter groups in the equal parameter case, and speculated that a similar result should hold in the unequal parameter case. We conjecture that the defect is a block invariant for all cyclotomic Hecke algebras associated with complex reflection groups, and we prove it for the groups of type G(l, p, n) and for the exceptional types for which the blocks are known. In particular, for the groups G(l, 1, n), we show that the defect corresponds to the notion of weight in the sense of Fayers, for which we thus obtain a new way of computation. We also prove that the defect is a block invariant for cyclotomic Yokonuma-Hecke algebras.

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Section: Defect In Cyclotomic Hecke Algebras Of Exceptional Groupsmentioning

confidence: 99%