Inventiones mathematicae

, Volume 106, Issue 1, pp 461–488

A Frobenius formula for the characters of the Hecke algebras

  • Arun Ram
Article

DOI: 10.1007/BF01243921

Cite this article as:
Ram, A. Invent Math (1991) 106: 461. doi:10.1007/BF01243921

Summary

This paper uses the theory of quantum groups and the quantum Yang-Baxter equation as a guide in order to produce a method of computing the irreducible characters of the Hecke algebra. This approach is motivated by an observation of M. Jimbo giving a representation of the Hecke algebra on tensor space which generates the full centralizer of a tensor power of the “standard” representation of the quantum group\(U_q (\mathfrak{s}l(n))\). By rewriting the solutions of the quantum Yang-Baxter equation for\(U_q (\mathfrak{s}l(n))\) in a different form one can avoid the quantum group completely and produce a “Frobenius” formula for the characters of the Hecke algebra by elementary methods. Using this formula we derive a combinatorial rule for computing the irreducible characters of the Hecke algebra. This combinatorial rule is aq-extension of the Murnaghan-Nakayama for computing the irreducible characters of the symmetric group. Along the way one finds connections, apparently unexplored, between the irreducible characters of the Hecke algebra and Hall-Littlewood symmetric functions and Kronecker products of symmetric groups.

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Arun Ram
    • 1
  1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA