Hecke Algebras of Type A at q = 0 and Quasi-differential Operators

  • Artem Yu. Golubkov
  • Roberto Mantaci
Conference paper

Abstract

In this paper we establish a noncommutative q-analogue of the Murnaghan-Nakayama rule and we provide a representation theoretic interpretation of some quasi-differential operators by giving a branching rule for indecomposable projective H n (0)-modules.

Keywords

Convolution Verse 

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References

  1. 1.
    G. Duchamp, A. Klyachko, D. Krob, J.Y. Thibon, Noncommutative symmetric functions III: Deformations of Cauchy and convolution algebras, Disc. Math. and Theor. Comput. Sci., 1, 1997, 159 - 216.MathSciNetMATHGoogle Scholar
  2. 2.
    I.M. Gelfand, D. Krob, A. Lascoux, B. Leclerc, V.S. Retakh, J.-Y. Thibon, Non-commutative symmetric functions, Adv. in Math. 112, (1995), 218 - 348.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    I. Gessel, Multipartite P-partitions and inner product of skew Schur functions, Con-temp. Math. 34, (1984), 289 - 301.Google Scholar
  4. 4.
    D. Krob, R. Mantaci, Noncommutative ribbons and quasi-differential operators, Publication L.I.A.F.A., Université Paris 7, Avr. 1999.Google Scholar
  5. 5.
    D. Krob, J.Y. Thibon, Noncommutative symmetric functions IV: Quantum linear groups and Hecke algebras at q = 0, J. of Mg. Comb., 6, (4), 339 - 376, 1997.MathSciNetMATHGoogle Scholar
  6. 6.
    I. G. Macdonald, Symmetric functions and Hall Polynomials, Oxford Math. Monographs, Oxford University Press, 2nd Ed., 1994.Google Scholar
  7. 7.
    C. Malvenuto, C. Reutenauer, Duality between quasi-symmetric functions and the Solomon descent algebra, J. Algebra 177, (1995), 967 - 982.MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    P. N. Norton, 0-Hecke algebras, J. Austral. Math. Soc. Ser. A, 27, 1979, 337 - 357.Google Scholar
  9. 9.
    C. Reutenauer, Lie Algebras, Oxford University Press, 1993.Google Scholar
  10. 10.
    G. de B. Robinson, Representation Theory of the Symmetric Group, University of Toronto Press, 1961.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Artem Yu. Golubkov
    • 1
  • Roberto Mantaci
    • 2
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.LIAFAUniversité Paris 7 — Denis DiderotParis Cedex 05France

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