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

  • Eirini ChavliEmail author
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Abstract

We determine all the decomposition matrices of the generic Hecke algebras on 3 strands in characteristic 0. These are the generic Hecke algebras associated with the exceptional complex reflection groups G4, G8, and G16. We prove that for every choice of the parameters that define these algebras, all simple representations of the specialized algebra are obtained as modular reductions of simple representations of the generic algebra.

Keywords

Representation theory Hecke algebras Braid group on 3 strands Complex reflection groups Decomposition matrices 

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Notes

Acknowledgements

I would like to thank T. Conde, M. Geck, S. König, J. Külshammer and U. Thiel for fruitful discussions and references. Moreover, I would like to thank J. Michel for suggesting working with powers of the parameters in GAP, and M. Chlouveraki and G. Pfeiffer for carefully reading this paper.

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Institut für Algebra und ZahlentheorieUniversität StuttgartStuttgartGermany

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