Noncommutative Symmetric Functions Iv: Quantum Linear Groups andHecke Algebras at {\bi q}\,{\bf =}\,{\bf 0}

  • Authors:

  • Daniel Krob;Jean-Yves Thibon

  • Affiliations:

  • LIAFA (CNRS), Université Paris 7, 2, place Jussieu, 75251 Paris Cedex 05, France. E-mail: dk@litp.ibp.fr;IGM, Université de Marne-la-Vallée, 2, rue de la Butte-Verte, 93166 Noisy-le-Grand Cedex, France. E-mail: jyt@univ-mlv.fr

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 1997

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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.