Algebras and Representation Theory

, Volume 20, Issue 2, pp 355–377 | Cite as

Modules for Yokonuma-type Hecke Algebras

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Abstract

This paper describes the module categories for a family of generic Hecke algebras, called Yokonuma-type Hecke algebras. Yokonuma-type Hecke algebras specialize both to the group algebras of the complex reflection groups G(r,1,n) and to the convolution algebras of (B \(^{\prime }\),B \(^{\prime }\))-double cosets in the group algebras of finite general linear groups, for certain subgroups B \(^{\prime }\) consisting of upper triangular matrices. In particular, complete sets of inequivalent, irreducible modules for semisimple specializations of Yokonuma-type Hecke algebras are constructed.

Keywords

Representation theory Hecke algebras Finite general linear groups Generic algebras 

Mathematics Subject Classification (2010)

Primary 20C08 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsRadford UniversityRadfordUSA

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