Timeline for Geometry of elements with prescribed multiplicity eigenvalues

6 events

when toggle format	what		by	license	comment
Apr 26, 2021 at 15:42	history	edited	Tommaso Scognamiglio	CC BY-SA 4.0	Explained more clearly what was the central question
Apr 23, 2021 at 16:09	comment	added	Sam Gunningham		In particular, if $L$ denotes the Levi in question (i.e. block matrices with blocks $(n_1, \ldots , n_k)$) and $\mathcal O$ denotes the corresponding unipotent orbit (unipotent block matrices with Jordan type $\lambda_1, \ldots , \lambda_k$), and $W$ denotes the the regular part of the center of the Levi as in your question, there is a conjugation map $G \times (W\times \mathcal O) \to G$ which surjects onto the locus you describe. This should be a torsor for the normalizer $N_G(L)$.
Apr 23, 2021 at 15:48	comment	added	Sam Gunningham		I believe what you are describing are called Lusztig strata (or at least are related to them). If I understand correctly, you have fixed a Levi of GL(n) and are looking at the union of conjugacy classes of elements whose semisimple part is a regular element of the center of the Levi, and the nilpotent part lives in a fixed nilpotent orbit of the Levi. I believe they are smooth. See, e.g. Section 3 of Lusztig's 1984 paper "Intersection cohomology complexes..." (which is written for a general reductive group).
Apr 23, 2021 at 14:45	history	edited	LSpice	CC BY-SA 4.0	Proofreading
Apr 23, 2021 at 12:37	history	edited	Tommaso Scognamiglio	CC BY-SA 4.0	added 34 characters in body
Apr 23, 2021 at 12:10	history	asked	Tommaso Scognamiglio	CC BY-SA 4.0