Isotypic decompositions and Hom schemes for algebraic groups

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• Sean Cotner (University of Michigan)
• Tuesday 15 July 2025, 15:30-16:30
• External.

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GCLW01 - Modular Lie theory

It is well-known that the representations of a finite group X are “the same” in characteristic zero as incharacteristic p >0, provided that p does not divide the order of X. A standard proof of this fact involvesestablishing the existence of isotypic decompositions for representations of X over discrete valuation rings.Attempting to generalize this latter result to representations valued in arbitrary reductive groups turns outto lead naturally to the consideration of schemes which parameterize homomorphisms between algebraicgroups, whose study was initiated by Grothendieck and Demazure. After motivating these objects, I willdescribe a relatively simple construction, as well as some applications and open questions if time permits. Partially based on work joint with Jeremy Booher and Shiang Tang

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

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