Israel Journal of Mathematics

, Volume 179, Issue 1, pp 381–402

A Gelfand model for wreath products

  • Ron M. Adin
  • Alexander Postnikov
  • Yuval Roichman


A Gelafand model for wreath products ℤrSn is constructed. The proof relies on a combinatorial interpretation of the characters of the model, extending a classical result of Frobenius and Schur.


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  1. [1]
    R. M. Adin, A. Postnikov and Y. Roichman, Combinatorial Gelfand Models, Journal of Algebra, to appear.Google Scholar
  2. [2]
    J. L. Aguado and J. O. Araujo, A Gelfand model for the symmetric group, Communications in Algebra 29 (2001), 1841–1851.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    J. O. Araujo, A Gelfand model for a Weyl group of type B n, Beitrzur Algebra und Geometrie 44 (2003), 359–373.MATHMathSciNetGoogle Scholar
  4. [4]
    J. O. Araujo and J. J. Bigeón, A Gelfand model for a Weyl group of type D n and the branching rules D nB n, Journal of Algebra 294 (2005), 97–116.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    R. W. Baddeley, Models and involution models for wreath products and certain Weyl groups, Journal of the London Mathematical Society. Second Series 44 (1991), 55–74.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    I. N. Bernstein, I. M. Gelfand and S. I. Gelfand, Models of representations of compact Lie groups (Russian), Funkcional. Anal. i Prilozen. 9 (1975), 61–62.CrossRefMathSciNetGoogle Scholar
  7. [7]
    D. Bump and D. Ginzburg, Generalized Frobenius-Schur numbers, Journal of Algebra 278 (2004), 294–313.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    G. Frobenius and I. Schur, Über die reellen Darstellungen de rendlichen Gruppen, S’ber. Akad. Wiss. Berlin (1906), 186–208.Google Scholar
  9. [9]
    R. Gow, Real representations of the finite orthogonal and symplectic groups of odd characteristic, Journal of Algebra 96 (1985), 249–274.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    N. F. J. Inglis, R. W. Richardson and J. Saxl, An explicit model for the complex representations of S n, Archiv der Mathematik. Birkhäuser, Basel 54 (1990), 258–259.MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    I. M. Isaacs, Character Theory of Finite Groups, Dover, New York, 1994.MATHGoogle Scholar
  12. [12]
    N. Kawanaka and H. Matsuyama, A twisted version of the Frobenius-Schur indicator and multiplicity-free permutation representation, Hokkaido Mathematical Journal 19 (1990), 495–508.MATHMathSciNetGoogle Scholar
  13. [13]
    A. A. Klyachko, Models for complex representations of the groups GL(n, q) and Weyl groups (Russian), Dokl. Akad. Nauk SSSR 261 (1981), 275–278.MathSciNetGoogle Scholar
  14. [14]
    A. A. Klyachko, Models for complex representations of groups GL(n, q) (Russian), Rossiĭskaya Akademiya Nauk. Matematicheskiĭ Sbornik (N.S.) 120(162) (1983), 371–386.MathSciNetGoogle Scholar
  15. [15]
    V. Kodiyalam and D.-N. Verma, A natural representation model for symmetric groups, preprint, 2004.Google Scholar
  16. [16]
    Y. Roichman, A recursive rule for Kazhdan-Lusztig characters, Advances in Mathematics 129 (1997), 24–45.CrossRefMathSciNetGoogle Scholar
  17. [17]
    P. D. Ryan, Representations of Weyl groups of type B induced from centralisers of involutions, Bulletin of the Australian Mathematical Society 44 (1991), 337–344.MATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    D. Stanton and D. E. White, A Schensted algorithm for rim hook tableaux, Journal of Combinatorial Theory. Series A 40 (1985), 211–247.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University Magnes Press 2010

Authors and Affiliations

  • Ron M. Adin
    • 1
  • Alexander Postnikov
    • 2
  • Yuval Roichman
    • 3
  1. 1.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael
  2. 2.Department of Applied MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  3. 3.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael

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