Two-row Delta Springer varieties - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Two-row Delta Springer varieties

Résumé

We study the geometry and topology of $\Delta$-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 $\Delta$-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 $\Delta$-Springer variety to an action of a degenerate affine Hecke algebra and relate this action to a $\mathfrak{gl}_{2}$-tensor space.
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Dates et versions

hal-04696282 , version 1 (12-09-2024)

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Abel Lacabanne, Pedro Vaz, Arik Wilbert. Two-row Delta Springer varieties. 2024. ⟨hal-04696282⟩
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