Quasi-semisimple elements

Abstract

We study quasi-semisimple elements of disconnected reductive algebraic groups over an algebraically closed field. We describe their centralizers, define isolated and quasi-isolated quasi-semisimple elements and classify their conjugacy classes.

Moduli of Langlands Parameters

“…Since Z(H P,• ) is an extension of Z((H ad ) P,• ) by K, we see that it suffices to prove that π 0 (Z((H ad ) P,• )) has p-power order. But Theorem 3.11 of [DM18] asserts that this order even divides the order p of the cyclic group P . Using Remark 3.9, we can now strengthen Theorem 3.4 for a certain class of groups, by replacing "Borel pair" by "pinning".…”

Unitriangular Shape of Decomposition Matrices of Unipotent Blocks

“…In this section we recall some recent results of [19] concerning quasi-semisimple elements. Let Σ ⊆ Φ be a closed subsystem with positive system Σ + ⊆ Σ and T 0 M G the corresponding subsystem subgroup.…”

“…Following [19] we say the orbit O is special if there exist two roots α, β ∈ O such that α + β ∈ Σ is a root. The orbit of α + β is then said to be cospecial.…”