Euler–Poincaré Characteristic and Polynomial Representations of Iwahori–Hecke Algebras

  • Gérard H. E. Duchamp

    Université Paris-Nord, Villetaneuse, France
  • Daniel Krob

    Université Paris 7, France
  • Alain Lascoux

    Université de Paris-Est, Marne-la-Vallée, France
  • Bernard Leclerc

    Université de Caen, France
  • Thomas Scharf

    Universität Bayreuth, Germany
  • Jean-Yves Thibon

    Universität Bayreuth, Germany


The Hecke algebras of type admit faithful representations by symmetrization operators acting on polynomial rings. These operators are related to the geometry of flag manifolds and in particular to a generalized Euler–Poincaré characteristic denned by Hirzebruch. They provide -idempotents, together with a simple way to describe the irreducible representations of the Hecke algebra. The link with Kazhdan–Lusztig representations is discussed. We specially detail the case of hook representations, and as an application, we investigate the hamiltonian of a quantum spin chain with symmetry.

Cite this article

Gérard H. E. Duchamp, Daniel Krob, Alain Lascoux, Bernard Leclerc, Thomas Scharf, Jean-Yves Thibon, Euler–Poincaré Characteristic and Polynomial Representations of Iwahori–Hecke Algebras. Publ. Res. Inst. Math. Sci. 31 (1995), no. 2, pp. 179–201

DOI 10.2977/PRIMS/1195164438