Symmetric functions for the generating matrix of Yangian of gl_n(C)

TL;DR

This paper explores symmetric functions related to the generating matrix of the Yangian of gl_n(C), extending classical combinatorial identities to this algebraic context and deriving new relations for shifted Schur functions.

Contribution

It introduces analogues of classical symmetric function identities within the framework of the Yangian of gl_n(C), providing new algebraic relations and extending combinatorial theory.

Findings

Derived identities for elementary and homogeneous symmetric functions in the Yangian context.

Established relations for shifted Schur functions based on these identities.

Extended classical combinatorial identities to a quantum algebra setting.

Abstract

Analogues of classical combinatorial identities for elementary and homogeneous symmetric functions with coefficients in Yanigian are discussed. As a corollary, similar relations are deduced for shifted Schur functions.