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Journal of Algebraic Combinatorics

, Volume 6, Issue 4, pp 339–376 | Cite as

Noncommutative Symmetric Functions Iv: Quantum Linear Groups and Hecke Algebras at q = 0

  • Daniel Krob
  • Jean-Yves Thibon
Article

Abstract

We present representation theoretical interpretations ofquasi-symmetric functions and noncommutative symmetric functions in terms ofquantum linear groups and Hecke algebras at q = 0. We obtain inthis way a noncommutative realization of quasi-symmetric functions analogousto the plactic symmetric functions of Lascoux and Schützenberger. Thegeneric case leads to a notion of quantum Schur function.

quasisymmetric function quantum group Hecke algebra 

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Daniel Krob
    • 1
  • Jean-Yves Thibon
    • 2
  1. 1.LIAFA (CNRS), Université Paris 7Paris Cedex 05France
  2. 2.IGM, Université de Marne-la-ValléeNoisy-le-Grand CedexFrance

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