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This content will become publicly available on December 3, 2025

Title: An inverse Grassmannian Littlewood–Richardson rule and extensions
Chow rings of flag varieties have bases of Schubert cycles \sigma_u, indexed by permutations. A major problem of algebraic combinatorics is to give a positive combinatorial formula for the structure constants of this basis. The celebrated Littlewood-Richardson rules solve this problem for special products \sigma_u \cdot \sigma_v where u and v are p-Grassmannian permutations. Building on work of Wyser, we introduce backstable clans to prove such a rule for the problem of computing the product \sigma_u \cdot \sigma_v when u is p-inverse Grassmannian and v is q-inverse Grassmannian. By establishing several new families of linear relations among structure constants, we further extend this result to obtain a positive combinatorial rule for \sigma_u \cdot \sigma_v in the case that u is covered in weak Bruhat order by a p-inverse Grassmannian permutation and v is a q-inverse Grassmannian permutation.  more » « less
Award ID(s):
2344764
PAR ID:
10609118
Author(s) / Creator(s):
;
Publisher / Repository:
Cambridge University Press
Date Published:
Journal Name:
Forum of Mathematics, Sigma
Volume:
12
ISSN:
2050-5094
Page Range / eLocation ID:
e114
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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