On the decomposition of tensor representations of symmetric groups

TL;DR

This paper explores a novel approach to decomposing tensor representations of symmetric groups into irreducible components, extending classical methods by involving two symmetric groups for greater explicitness.

Contribution

It introduces a new framework using two symmetric groups to clarify the decomposition of tensor representations, advancing understanding of symmetric group representations.

Findings

Explicit decomposition formulas for tensor representations.

Enhanced understanding of symmetric group representation structure.

Potential applications to infinite symmetric groups.

Abstract

Following the general idea of Schur--Weyl scheme and using two suitable symmetric groups (instead of one), we try to make more explicit the classical problem of decomposing tensor representations of finite and infinite symmetric groups into irreducible components.