# A construction by deformation of unitary irreducible representations of $SU(1,n)$ and $SU(n+1)$

## TL;DR

This paper presents a method to derive certain unitary irreducible representations of $SU(1,n)$ and $SU(n+1)$ through deformation of minimal realizations of their Lie algebra, enriching the understanding of their representation theory.

## Contribution

It introduces a deformation approach to construct holomorphic discrete series and other unitary irreducible representations of these groups.

## Key findings

- Holomorphic discrete series of $SU(1,n)$ are recovered.
- Some unitary irreducible representations of $SU(n+1)$ are obtained.
- The method provides a new perspective on the representation theory of these groups.

## Abstract

We recover the holomorphic discrete series representations of $SU(1,n)$ as well as some unitary irreducible representations of $SU(n+1)$ by deformation of a minimal realization of $sl(n+1, {\mathbb C})$.