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no. 4
Two-row Delta Springer varieties
Lacabanne, Abel1; Vaz, Pedro2; Wilbert, Arik3
1 Laboratoire de Mathématiques Blaise Pascal (UMR 6620) Université Clermont Auvergne Campus Universitaire des Cézeaux 3 place Vasarely 63178 Aubière Cedex France
2 Institut de Recherche en Mathématique et Physique Université Catholique de Louvain Chemin du Cyclotron 2 1348 Louvain-la-Neuve Belgium
3 Department of Mathematics & Statistics University of South Alabama Mobile AL 36688 USA
Algebraic Combinatorics, Volume 8 (2025) no. 4, pp. 925-953.

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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.435
Classification: 14M15, 05E10, 20C08
Keywords: Springer theory, flag varieties, action on homology, degenerate affine Hecke algebra

Lacabanne, Abel 1; Vaz, Pedro 2; Wilbert, Arik 3

1 Laboratoire de Mathématiques Blaise Pascal (UMR 6620) Université Clermont Auvergne Campus Universitaire des Cézeaux 3 place Vasarely 63178 Aubière Cedex France
2 Institut de Recherche en Mathématique et Physique Université Catholique de Louvain Chemin du Cyclotron 2 1348 Louvain-la-Neuve Belgium
3 Department of Mathematics & Statistics University of South Alabama Mobile AL 36688 USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Lacabanne, Abel; Vaz, Pedro; Wilbert, Arik. Two-row Delta Springer varieties. Algebraic Combinatorics, Volume 8 (2025) no. 4, pp. 925-953. doi : 10.5802/alco.435. https://alco.centre-mersenne.org/articles/10.5802/alco.435/

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