Strong asymptotic freeness for free orthogonal quantum groups

TL;DR

This paper proves that the generators of free orthogonal quantum groups become asymptotically free semicircular systems as the dimension grows, with similar results for free unitary quantum groups, impacting quantum algebra understanding.

Contribution

It establishes strong asymptotic freeness results for free orthogonal and unitary quantum groups as their size increases, extending free probability theory.

Findings

Generators converge strongly to free semicircular systems

Results apply to free unitary quantum groups

Provides applications in quantum algebra

Abstract

We prove that the normalized standard generators of the free orthogonal quantum group $O_N^+$ converge strongly to a free semicircular system as $N \to \infty$. Analogous results are obtained for the free unitary quantum groups, and some applications are given.