Modular finite W-algebras

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Authors

Colleges, School and Institutes

Abstract

Let k be an algebraically closed field of characteristic p > 0 and let G be a connected reductive algebraic group over k. Under some standard hypothesis on G, we give a direct approach to the finite W-algebra U(g,e) associated to a nilpotent element e ∈ g = Lie G. We prove a PBW theorem and deduce a number of consequences, then move on to define and study the p-centre of U(g,e), which allows us to define reduced finite W-algebras Un (g,e) and we verify that they coincide with those previously appearing in the work of Premet. Finally, we prove a modular version of Skryabin's equivalence of categories, generalizing recent work of the second author.

Details

Original languageEnglish
Pages (from-to)5811–5853
Number of pages43
JournalInternational Mathematics Research Notices
Volume2019
Issue number18
Early online date16 Jan 2018
Publication statusPublished - Sep 2019