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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Representations of graded Hecke algebras
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by Cathy Kriloff and Arun Ram
Represent. Theory 6 (2002), 31-69
Published electronically: May 2, 2002


Representations of affine and graded Hecke algebras associated to Weyl groups play an important role in the Langlands correspondence for the admissible representations of a reductive $p$-adic group. We work in the general setting of a graded Hecke algebra associated to any real reflection group with arbitrary parameters. In this setting we provide a classification of all irreducible representations of graded Hecke algebras associated to dihedral groups. Dimensions of generalized weight spaces, Langlands parameters, and a Springer-type correspondence are included in the classification. We also give an explicit construction of all irreducible calibrated representations (those possessing a simultaneous eigenbasis for the commutative subalgebra) of a general graded Hecke algebra. While most of the techniques used have appeared previously in various contexts, we include a complete and streamlined exposition of all necessary results, including the Langlands classification of irreducible representations and the irreducibility criterion for principal series representations.
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Bibliographic Information
  • Cathy Kriloff
  • Affiliation: Department of Mathematics, Idaho State University, Pocatello, Idaho 83209-8085
  • MR Author ID: 630044
  • ORCID: 0000-0003-2863-6724
  • Email:
  • Arun Ram
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • MR Author ID: 316170
  • Email:
  • Received by editor(s): May 15, 2001
  • Received by editor(s) in revised form: December 21, 2001, and January 23, 2002
  • Published electronically: May 2, 2002
  • Additional Notes: Research of the first author supported in part by an NSF-AWM Mentoring Travel Grant
    Research of the second author supported in part by National Security Agency grant MDA904-01-1-0032 and EPSRC Grant GR K99015
  • © Copyright 2002 American Mathematical Society
  • Journal: Represent. Theory 6 (2002), 31-69
  • MSC (2000): Primary 20C08; Secondary 16G99
  • DOI:
  • MathSciNet review: 1915086