Algebra Seminar: Abel Lacabanne -- Two-row Delta Springer varieties and representations of the degenerate affine Hecke algebra

Welcome back!  

Abel Lacabanne (Universite Clermont Auvergne) is speaking in the Algebra Seminar this
week.  We will go out for lunch after the talk.  

When: Friday 9 August, 12-1pm 

Where: Carslaw 275 (Note location!) 

Title: Two-row Delta Springer varieties and representations of the degenerate affine
Hecke algebra 

Abstract: Delta Springer varieties were recently introduced by Griffin--Lewinson--Woo to
provide a geometric setting for a conjecture of Haglund--Remmel--Wilson on certain
symmetric functions.  These varieties are defined using a partition of an integer, and
in this talk, I will focus on the case of two-row partitions.  It turns out that the
geometry of these two-row Delta Springer varieties has a nice diagrammatic
interpretation using a variant of crossingless matchings.  Griffin--Lewinson--Woo also
constructed an action of the symmetric group on the top degree cohomology of Delta
Springer varieties.  In the two-row case, I will give a skein-theoretic interpretation
of this action, and enhance it to an action of the degenerate affine Hecke algebra.
These representations can also be retrived via the action of the Lie algebra sl2 on some
tensor space.  

This is joint work with Pedro Vaz and Arik Wilbert.