Journal of Algebraic Combinatorics

, Volume 47, Issue 2, pp 175–211 | Cite as

The irreducible characters of the alternating Hecke algebras

  • Andrew Mathas
  • Leah Neves


This paper computes the irreducible characters of the alternating Hecke algebras, which are deformations of the group algebras of the alternating groups. More precisely, we compute the values of the irreducible characters of the semisimple alternating Hecke algebras on a set of elements indexed by minimal length conjugacy class representatives and we show that these character values determine the irreducible characters completely. As an application, we determine a splitting field for the alternating Hecke algebras in the semisimple case.


Iwahori–Hecke algebras Alternating groups Characters 



We thank the referee for their thorough reading of our manuscript and for their many corrections. This research was supported, in part, by the Australian Research Council. Some of the results in this paper appear in the second author’s Ph.D. thesis [18].


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia

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