Affine Bruhat order and Demazure products
Felix Schremmer
TL;DR
This paper introduces new descriptions of the affine Bruhat order and Demazure products using the quantum Bruhat graph's weight function, with applications to affine Deligne-Lusztig varieties and Newton points.
Contribution
It provides novel characterizations of affine Bruhat order and Demazure products through the quantum Bruhat graph, enhancing understanding of algebraic group decompositions.
Findings
New formulas for affine Bruhat order and Demazure products
Applications to affine Deligne-Lusztig varieties and Newton points
Enhanced understanding of Iwahori-Bruhat decomposition
Abstract
We give new descriptions of the Bruhat order and Demazure products of affine Weyl groups in terms of the weight function of the quantum Bruhat graph. These results can be understood to describe certain closure relations concerning the Iwahori-Bruhat decomposition of an algebraic group. As an application towards affine Deligne-Lusztig varieties, we present a new formula for generic Newton points.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Combinatorial Mathematics · Advanced Mathematical Identities