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Demazure product of the affine Weyl groups
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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
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The Quantum Bruhat Graph for $\widehat{SL}_2$ and Double Affine Demazure Products
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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