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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 *Y*_{n,λ,s} generalizing the type *A* Springer fibers, whose cohomology rings have the structure of an *S*_{n}-module. We give an explicit presentation for the cohomology ring *H*^{*}(*Y*_{n,λ,s};**Q**), and we find an affine paving of *Y*_{n,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 *Y*_{n,λ,s} give a generalization of the type A Springer correspondence to the setting of induced Specht modules.
Furthermore, the special case
*Y*_{n,(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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