Let G be a non-connected reductive algebraic group over an algebraically closed field K and let D be a connected component of G. We investigate the Jordan classes of D and we obtain a description of the regular part of the closure of a Jordan class in terms of induction of G∘-orbits. We use this result to show that Lusztig strata in a non-connected reductive algebraic group are locally closed.
Jordan classes and Lusztig strata in disconnected reductive groups
Martina Costa Cesari
2023
Abstract
Let G be a non-connected reductive algebraic group over an algebraically closed field K and let D be a connected component of G. We investigate the Jordan classes of D and we obtain a description of the regular part of the closure of a Jordan class in terms of induction of G∘-orbits. We use this result to show that Lusztig strata in a non-connected reductive algebraic group are locally closed.
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