Exotic Springer Fibers for Orbits Corresponding to One-Row Bipartitions

Saunders, Neil; Wilbert, Arik

doi:10.1007/s00031-020-09613-0

Cited by 2 publications

(8 citation statements)

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“…As in Theorem 4.1, we compare a two-row ∆-Springer variety with an exotic Springer fiber associated with a onerow bipartition. Before doing so, let us recall the description of [SaWi22] of the irreducible components of exotic Springer fibers for one-row bipartitions.…”

Section: 2mentioning

confidence: 99%

“…are described by flags in Y n−m and so are the elements of the exotic Springer fiber B e ((n−m−k),(k)) . We quickly recall the diagrammatics describing the irreducible components of the exotic Springer fiber associated with the bipartition ((n − m − k), (k)), see [SaWi22] for more details. These irreducible components are indexed by one-boundary diagrams on n − m points which are endpoints of rays, cups or half-cups: cups connect two points, and both rays and halfcups connect only one point.…”

Section: 2mentioning

confidence: 99%

“…The exotic Springer fibers associated with one-row bipartitions share many geometric properties with the ordinary two-row Springer fibers in type A. Also note that the combinatorics of the blob algebra naturally appear when studying exotic Springer fibers for one-row bipartitions, [SaWi22].…”

Section: Introductionmentioning

confidence: 99%

“…In the exotic case, the nilpotent orbits have been classified explicitly using bipartitions [AcHe08]. The irreducible components of exotic Springer fibers have been studied thoroughly in [NRS18], as well as [SaWi22] in the specific case of one-row bipartitions. As for the ordinary two-row Springer fibers, the irreducible components of exotic Springer fibers for one-row bipartitions can be described using certain cup diagrams.…”

Section: Introductionmentioning

confidence: 99%

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Lacabanne

Vaz

2021

Pacific J. Math.

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We study the geometry and topology of ∆-Springer varieties associated with tworow 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 ∆-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 ∆-Springer variety to an action of a degenerate affine Hecke algebra and relate this action to a gl 2 -tensor space. CONTENTS 1. Introduction 1 2. ∆-Springer varieties 5 3. Irreducible components for two-row ∆-Springer varieties 9 4. Comparison with Springer fibers and exotic Springer fibers 14 5. A topological model and the action of the symmetric group 16 6. Action of the degenerate affine Hecke algebra 20 References 30

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Section: 2mentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%