On the reductive monoid associated to a parabolic subgroup

2016/02/23 by Jonathan Wang, Wang, Jonathan · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1602.07233

15 pages

arxiv created 2016/02/23 · openalex publication_date 2016/02/23 · arxiv updated 2016/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a connected reductive group over a perfect field k. We study a certain normal reductive monoid M associated to a parabolic k-subgroup P of G. The group of units of M is the Levi factor M of P. We show that M is a retract of the affine closure of the quasi-affine variety G/U(P). Fixing a parabolic P^- opposite to P, we prove that the affine closure of G/U(P) is a retract of the affine closure of the boundary degeneration (G × G)/(P ×_M P^-). Using idempotents, we relate M to the Vinberg semigroup of G. The monoid M is used implicitly in the study of stratifications of Drinfeld's compactifications of the moduli stacks Bun_P and Bun_G.

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• Geometric Bernstein Asymptotics and the Drinfeld-Lafforgue-Vinberg degeneration for arbitrary reductive groups

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