Two-row Delta Springer varieties

Data

• Title: Two-row Delta Springer varieties
• Authors: Abel Lacabanne, Pedro Vaz and Arik Wilbert
• arXiv link: https://arxiv.org/abs/2407.10792
• Published in: Algebr. Comb. 8 (2025), no. 4, pp. 925–953.
• DOI: 10.5802/alco.435

Abstract

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.

Citation

@article {MR4952053,
    AUTHOR = {Lacabanne, Abel and Vaz, Pedro and Wilbert, Arik},
     TITLE = {Two-row {D}elta {S}pringer varieties},
   JOURNAL = {Algebr. Comb.},
  FJOURNAL = {Algebraic Combinatorics},
    VOLUME = {8},
      YEAR = {2025},
    NUMBER = {4},
     PAGES = {925--953},
      ISSN = {2589-5486},
   MRCLASS = {14M15},
  MRNUMBER = {4952053},
       DOI = {10.5802/alco.435},
       URL = {https://doi.org/10.5802/alco.435},
}