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Demazure product of the affine Weyl groups

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arxiv 2112.06376 v1 pith:UCVN7OQJ submitted 2021-12-13 math.RT math.AG

classification math.RTmath.AG
keywords demazureweylgroupproductaffineexplicitextendedobtain
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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 $\tilde W$. 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/shrunken Weyl chambers of $\tilde W$, and obtain an explicit formula on the Lusztig-Vogan map from the coweight lattice to the set of dominant coweights.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Quantum Bruhat Graph for $\widehat{SL}_2$ and Double Affine Demazure Products

    math.RT 2024-11 conditional novelty 6.0 of 10

    For type SL2-hat, the quantum Bruhat graph formula for the Demazure product on the double affine Weyl semigroup is well-defined for positive levels and associative for levels greater than one.

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