Work

Action of W$W$‐type operators on Schur functions and Schur Q‐functions

Year: 2025

Type: article

Abstract: In this paper, we investigate a series of W‐type differential operators, which appear naturally in the symmetry algebras of KP and BKP hierarchies. In particular, they include all operators in the W‐constraints for tau‐functions of higher KdV hierarchies that satisfy the string equation. We will give simple uniform formulas for actions of these operators on all ordinary Schur functions and Schur Q‐functions. As applications of such formulas, we will give new simple proofs for Alexandrov's conjecture and Mironov–Morozov's formula, which express the Brézin–Gross–Witten and Kontsevich–Witten tau‐functions as linear combinations of Q‐functions with simple coefficients, respectively.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70080

Authors: Xiaobo Liu, Chenglang Yang

Institutions: Peking University, Chinese Academy of Sciences, Academy of Mathematics and Systems Science

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G1666994247, G335815763, G5276749214, G8533620077