Modular Reduction of Nilpotent Orbits

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• Jay Taylor (University of Manchester)
• Tuesday 15 July 2025, 11:15-12:15
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GCLW01 - Modular Lie theory

We consider a split connected reductive algebraic Z-group Gand V a G-module which is either the Lie algebrag or its dual. If k is an algebraically closed field then, by base change, we get a group Gk and a correspondingmodule Vk. Hesselink has defined a partition of the nullcone N (Vk) of Vk into strata N (Vk | O) which canbe indexed, thanks to Clarke–Premet, by G©-orbits O ⊆ N (gC), such that N (gC | O) = O. Each stratumis a union of G(k)-orbits. In this talk I will describe joint work with Adam Thomas (Warwick) which produces for each orbit O ⊆ N (gC),via a case-by-case analysis, integral representatives e ∈ V ∩ N (Vk | O) whose reduction ek ∈ N (Vk | O)is well-behaved for every algebraically closed field k.

This talk is part of the Isaac Newton Institute Seminar Series series.

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