What question did this study set out to answer?

This research examines a normal reductive monoid associated with a parabolic subgroup in a connected reductive group over a perfect field.

March 29, 2026Open Access

On the Reductive Monoid Associated to a Parabolic Subgroup

JWJ. -F. WangGuilin University of Electronic Technology

Puntos clave

This research examines a normal reductive monoid associated with a parabolic subgroup in a connected reductive group over a perfect field.
Studied the normal reductive monoid related to parabolic subgroups.
Analyzed the group of units of the monoid as the Levi factor.
Proved the retract properties of affine closures of varieties related to the monoid.
Utilized idempotents to connect the monoid with the Vinberg semigroup.
Investigated implications for stratifications in moduli stacks.
Established that the reductive monoid is a retract of an affine closure.
Demonstrated relationships between different affine closures and boundary degenerations.
Connected the monoid to the Vinberg semigroup, enhancing its geometric interpretation.

Resumen

Let G be a connected reductive group over a perfect field k .We study a certain normal reductive monoid M associated to a parabolic ksubgroup 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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