Two-row Delta Springer varieties

Abstract

We study the geometry and topology of $\hat{I}”$-Springer varieties associated with two-row partitions. These varieties were introduced in recent work by Griffin-Levinson-Woo to give a geometric realization of a symmetric function appearing in the Delta conjecture by Haglund-Remmel-Wilson. We provide an explicit and combinatorial description of the irreducible components of the two-row $\hat{I}”$-Springer variety and compare it to the ordinary two-row Springer fiber as well as Kato's exotic Springer fiber corresponding to a one-row bipartition. In addition to that, we extend the action of the symmetric group on the homology of the two-row $\hat{I}”$-Springer variety to an action of a degenerate affine Hecke algebra and relate this action to a ${\mathfrak{gl}}_2$-tensor space.

v1: 32 pages, many figures, comments welcome; v2: 33 pages, many figures, reviewed version accepted in Algebraic Combinatorics, Theorem 4.1 was wrong and replaced by a counterexample