# Stability of the Heisenberg Product on Symmetric Functions

## TL;DR

This paper proves a stability property for the Heisenberg product of Schur functions, extending known results about the Kronecker product's stabilization to a broader algebraic context.

## Contribution

It establishes a new stability theorem for the Heisenberg product of Schur functions, generalizing Murnaghan's classical result.

## Key findings

- Heisenberg product stabilizes similarly to the Kronecker product.
- Provides a new algebraic stability result for symmetric functions.
- Extends classical stability theorems to a broader product.

## Abstract

The Heisenberg product is an associative product defined on symmetric functions which interpolates between the usual product and the Kronecker product. In 1938, Murnaghan discovered that the Kronecker product of two Schur functions stabilizes. We prove an analogous result for the Heisenberg product of Schur functions.