Polynomial divided difference operators satisfying the braid relations
Abstract
Abstract Many interesting families of polynomials are indexed by permutations or related objects, and are defined by applying divided difference operators, modified by polynomials, on some initial base case. The fact that these constructions produce well-defined polynomials is based on the applied modified divided difference operators satisfying the braid relations. We thus determine all the families of polynomial divided difference operators that satisfy the braid relations, complementing an old result of Lascoux and Schützenberger.
Fields of Study & Subjects
Holomorphic and Operator Theory
Publication details
- Journal / source
- Journal of Algebraic Combinatorics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 64
- Issue
- 1
- Publication date
- 13 June 2026
- Language
- EN