Tensor Powers of the Defining Representation of $S_n$

TL;DR

This paper provides a decomposition formula for tensor powers of the defining representation of the symmetric group $S_n$ and uses it to analyze the mixing time of a related Markov chain.

Contribution

It introduces a new decomposition formula for tensor powers of the defining representation of $S_n$ and applies it to bound the mixing time of a specific Markov chain.

Findings

Derived a decomposition formula for tensor powers of the defining representation.

Bounded the mixing time of a Markov chain on $S_n$ using the new formula.

Provided insights into the representation theory of $S_n$ and its applications.

Abstract

We give a decomposition formula for tensor powers of the defining representation of $S_n$ and apply it to bound the mixing time of a Markov chain on $S_n$.