Combinatorics & algebra seminar-The geometry of Hessenberg and Lusztig varieties

Title: The geometry of Hessenberg and Lusztig varieties

 

Abstract:  Hessenberg and Lusztig varieties are two families of closed subvarieties of generalized flag varieties with representation theoretic significance. In the case of Hessenberg varieties, one associates to a combinatorial piece of data a family of varieties living over the Lie algebra of a reductive group G. (For the general linear group, that combinatorial piece of data is just an integer-valued function. In general, it can be thought of as a G-equivariant subbundle of the tangent bundle of the flag variety.) In the case of Lusztig varieties, one associates to each element of the Weyl group of G a family of varieties over G. I'll talk about some basic results on the geometry of Hessenberg varieties. Then I'll state a theorem on the automorphisms of deformations of Hessenberg varieties. Finally, I'll state a theorem about the relationship between Hessenberg and Lusztig varieties.