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Some non-trivial Kazhdan-Lusztig coefficients of an affine Weyl group of type à n

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Abstract

In this paper we show that the leading coefficient µ(y,w) of some Kazhdan-Lusztig polynomials P y,w with y,w in an affine Weyl group of type à n is n + 2. This fact has some consequences on the dimension of first extension groups of finite groups of Lie type with irreducible coefficients.

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Authors and Affiliations

  1. Department of Mathematics, University of Virginia, Charlottesville, VA, 22903, USA

    Leonard Scott

  2. Hua Loo-Keng Key Laboratory of Mathematics and Institute of Mathematics, Chinese Academy of Sciences, Beijing, 100190, China

    NanHua Xi

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  1. Leonard Scott
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  2. NanHua Xi
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Correspondence to NanHua Xi.

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Scott, L., Xi, N. Some non-trivial Kazhdan-Lusztig coefficients of an affine Weyl group of type à n . Sci. China Math. 53, 1919–1930 (2010). https://doi.org/10.1007/s11425-010-4041-4

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  • DOI: https://doi.org/10.1007/s11425-010-4041-4

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