A note on representations of $SL_n$

TL;DR

This paper examines irreducible unitary representations of lower-rank special linear groups using matrix models, reviewing prior work and adding new calculations based on established theories.

Contribution

It provides a review of existing literature and introduces new calculations related to representations of $SL_n$ using matrix models.

Findings

Comprehensive review of existing representations

New calculations enhancing understanding of $SL_n$ representations

Clarification of matrix model applications

Abstract

In this note, we study irreducible unitary representations of special linear groups of lower ranks, in terms of the matrix models of Gelfand-Naimark and Gelfand-Graev. Review of existing literature is provided. We also add some new calculation based on existing theory.