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Irreducible Representations of Hecke Algebras of Type An and Lascoux-Schutzenberger Algorithm

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  • Lascoux-Schutzenbergerの算法によるHecke環の線形表現の構成
  • Lascoux Schutzenberger ノ サンポウ ニ ヨル Heckeカン ノ センケイ ヒョウゲン ノ コウセイ

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Abstract

In this paper, we will construct the W-graphs corresponding to the irreducible representation of Hecke algebra H(q,n). The algorithm used is based on Lascoux-Schuetzenberger's method. We have constructed all the irreducible representations of H(q,n) for n up to 17. The sesult show that the 0-1 conjecture for the value of μ(x,y), i.e. μ(x,y) should be 0 or 1, is not true. This means that the leading coefficients of the Kazhdan-Lusztig Polynomial may have values greater than 1.

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