Demazure Product of the Affine Weyl Groups

Xu Hua HE, Si An NIE

Acta Mathematica Sinica, Chinese Series ›› 2024, Vol. 67 ›› Issue (2) : 296-306.

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Acta Mathematica Sinica, Chinese Series ›› 2024, Vol. 67 ›› Issue (2) : 296-306. DOI: 10.12386/A20220172

Demazure Product of the Affine Weyl Groups

  • Xu Hua HE1, Si An NIE2
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Abstract

The Demazure product gives a natural monoid structure on any Coxeter group. Such structure occurs naturally in many different areas in Lie Theory. This paper studies the Demazure product of an extended affine Weyl group. The main discovery is a close connection between the Demazure product of an extended affine Weyl group and the quantum Bruhat graph of the finite Weyl group. As applications, we obtain explicit formulas on the generic Newton points and the Demazure products of elements in the lowest two-sided cell, and obtain an explicit formula on the LusztigVogan map from the coweight lattice to the set of dominant coweights.

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affine Weyl group / Demazure product / quantum Bruhat graph

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Xu Hua HE, Si An NIE. Demazure Product of the Affine Weyl Groups. Acta Mathematica Sinica, Chinese Series, 2024, 67(2): 296-306 https://doi.org/10.12386/A20220172

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