Springer Fibres, Stacking Maps & Partial Flag Varieties
ABSTRACT
The fibres coming from the Springer resolution on the nilpotent cone are incredibly rich algebraic varieties that have many applications in algebraic geometry, representation theory and combinatorics. In this talk, I will describe how we can use the combinatorics of (bi)tableaux to describe their geometry in low dimensions, and in particular, give a description of their irreducible components. I will also describe a map of Springer fibres resulting from the Lusztig-Spaltenstein construction of parabolic induction from a Levi subalgebra. This is joint work with Lewis Topley, and separately with Mee Seong Im and Arik Wilbert. Time permitting, I will also talk about recent work with Daniele Rosso, extending some of these results to the case of partial flag varieties.
