Séminaire Lotharingien de Combinatoire, 95B.97 (2026), 12 pp.
Raymond Chou and Mitsuki Hanada
A Descent Basis for the Δ-Springer Module
Abstract.
We give a descent monomial basis of Δ-Springer
modules Rn,λ,s, first
defined by Griffin (2021). Our construction simultaneously
generalizes the descent basis for the Garsia-Procesi
module Rλ (Carlsson-C. (2024), H.(2025)),
as well as the descent basis for the generalized coinvariant
algebras Rn,k studied by
Haglund-Rhoades-Shimozono (2018). We highlight the representation
theoretic properties of this monomial basis by using it to give a
direct combinatorial proof of the formula for graded Frobenius
character of Rn,λ,s in terms
of battery-powered tableaux, a fact which has only the geometric
proof of Gillespie-Griffin (2024).
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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