Result: Two-row Delta Springer varieties
Title:
Two-row Delta Springer varieties
Authors:
Contributors:
UCL - SST/IRMP - Institut de recherche en mathématique et physique, Lacabanne, Abel
Source:
Algebraic combinatorics, Vol. 8, no. 4, p. 925-953 (2025)
Publication Status:
Preprint
Publisher Information:
Cellule MathDoc/Centre Mersenne, 2025.
Publication Year:
2025
Subject Terms:
[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA], Representation Theory, action on homology, Springer theory, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Quantum Algebra, Combinatorics, flag varieties, Primary: 14M15, Secondary: 05E10, 20C08, FOS: Mathematics, Quantum Algebra (math.QA), Combinatorics (math.CO), [MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT], Representation Theory (math.RT), degenerate affine Hecke algebra
Document Type:
Academic journal
Article
File Description:
application/pdf
Language:
English
ISSN:
2589-5486
DOI:
10.5802/alco.435
DOI:
10.48550/arxiv.2407.10792
Rights:
CC BY
arXiv Non-Exclusive Distribution
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....d10cae616e1442a38f0b80aad16ae08b
Database:
OpenAIRE
Further Information
We study the geometry and topology of Δ-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 Δ-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 Δ-Springer variety to an action of a degenerate affine Hecke algebra and relate this action to a 𝔤𝔩 2 -tensor space.