On a relation between certain character values of symmetric groups and its connection with creation operators of symmetric functions

TL;DR

This paper explores new relations between symmetric group character values using maya diagrams, connecting them with creation operators for symmetric functions and extending to related algebraic structures.

Contribution

It introduces novel relations between symmetric group characters and creation operators, linking combinatorial and algebraic frameworks for symmetric functions and their generalizations.

Findings

Derived a new relation between symmetric group characters and maya diagrams.

Connected character relations with Bernstein's creation operators for Schur functions.

Extended the relations to projective characters and other algebraic structures.

Abstract

In this paper, we derive a relation of new kind between certain character values of symmetric groups in terms of so-called maya diagrams. We also investigate a relation between our result and Bernstein's creation operators for Schur functions, and consider analogous relations for projective characters of symmetric groups through creation operators for Schur $Q$-functions. We also consider analogous relations for characters of Brauer algebras and walled Brauer algebras.