Tensor powers of representations of (diagram) monoids

TL;DR

This paper investigates how tensor powers of representations of finite monoids, especially diagram monoids like Temperley-Lieb, Motzkin, and Brauer, grow in complexity and decomposability, providing explicit data and pattern analysis.

Contribution

It offers new explicit computations and pattern insights into the tensor power decompositions of representations of diagram monoids.

Findings

Explicit character tables for specific diagram monoids.

Patterns in the growth of indecomposable summands.

Analysis of decomposition behavior in tensor powers.

Abstract

We study tensor powers of representations of finite monoids, focusing on the growth behavior of their composition length and the number of indecomposable summands. Special attention is given to diagram monoids such as the Temperley-Lieb, Motzkin, and Brauer monoids. For these examples, we compute explicit data, including some character tables, and analyze patterns in the decomposition of their tensor powers.