Israel Journal of Mathematics

, Volume 229, Issue 1, pp 67–83 | Cite as

Characters of Iwahori–Hecke algebras

  • Deke ZhaoEmail author


In this paper we prove a quantum generalization of Regev’s theorems (Israel. J. Math. 195 (2013), 31–35) by applying the Schur–Weyl duality between the quantum superalgebra and Iwahori–Hecke algebra. We also present an alternative proof of the quantized generalizations using the skew character theory of Iwahori–Hecke algebras.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. M. Adin, A. Postnikov and Y. Roichman, Hecke algebra ations on the coinvariant algebra, Journal of Algebra 233 (2000), 594–613.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    G. Benkart, S.-J. Kang and M. Kashiwara, Crystal bases for the quantum superalgebra Uq(gl(m, n)), Journal of the American Mathematical Society 13 (2000), 293–331.zbMATHGoogle Scholar
  3. [3]
    A. Berele and A. Regev, Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras, Advances in Mathematics 64 (1987), 118–175.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    F. M. Goodman and H. Wenzl, Littlewood–Richardson coefficients for Hecke algebras at roots of unity, Advances in Mathematics 82 (1990), 244–265.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    P. N. Hoefsmit, Representations of Hecke algebras of finite group with BN-pairs of classical type, Thesis, University of British Columbia, 1974.Google Scholar
  6. [6]
    G. James and A. Kerber, The Representation Theory of the Symmetric Group, Encyclopedia of Mathematics and its Applications, Vol. 16, Addison-Wesley, Reading, MA, 1981.Google Scholar
  7. [7]
    M. Jimbo, A q-analogue of U(gl(N +1)), Hecke algebra, and the Yang–Baxter equation, Letters in Mathematical Physics 11 (1986), 247–252.CrossRefzbMATHGoogle Scholar
  8. [8]
    R. C. King and B. G. Wybourne, Representations and traces of the Hecke algebras Hn(q) of type An-1, Journal of Mathematical Physics 33 (1992), 4–14.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    H. Mitsuhashi, Schur–Weyl reciprocity between the quantum superalgebra and the Iwahori-Heke algebra, Algebras and Representation Theory 9 (2006), 309–322.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    D. Moon, Highest weight vectors of irreducible representations of the quantum superalgebra Uq(gl(m, n)), Journal of the Korean Mathematical Society 40 (2003), 1–28.CrossRefzbMATHGoogle Scholar
  11. [11]
    G. Pfeiffer, Young characters on Coxeter basis elements of Iwahori–Hecke algebras and a Murnaghan–Nakayam formula, Journal of Algebra 168 (1994), 525–535.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    A. Ram, A Frobenius formula for the characters of the Hecke algebra, Inventiones Mathematicae 106 (1991), 461–488.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    A. Regev, Lie superalgebras and some characters of Sn, Israel. Journal of Mathematics 195 (2013), 31–35.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    J. Taylor, A note on skew characters of symmetric groups, Israel Journal of Mathematics 221 (2017), 435–443.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.School of Applied MathematicsBeijing Normal University at ZhuhaiZhuhaiChina

Personalised recommendations