Séminaire Lotharingien de Combinatoire, 85B.76 (2021), 12 pp.

Sean T. Griffin, Jake Levinson and Alexander Woo

Springer Fibers and the Delta Conjecture at t=0

Abstract. We define a family of varieties Yn,λ,s generalizing the type A Springer fibers, whose cohomology rings have the structure of an Sn-module. We give an explicit presentation for the cohomology ring H*(Yn,λ,s;Q), and we find an affine paving of Yn,λ,s that is in bijection with a collection of partial row-strict fillings of a partition shape. We also prove that the top cohomology groups of Yn,λ,s give a generalization of the type A Springer correspondence to the setting of induced Specht modules. Furthermore, the special case Yn,(1k),k of our variety gives a new geometric realization of the representation corresponding to the expression in the Delta Conjecture when t=0.

Received: December 1, 2020. Accepted: March 1, 2021. Final version: April 29, 2021.

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