Computing the Haar state on ${\mathbb{O}(SL_q(3))}$

Ting Lu

paper

Computing the Haar state on $O (S L_{q} (3))$

arXiv:2301.12683

Abstract

This paper shows that to compute the Haar state on $O (S L_{q} (n))$ , it suffices to compute the Haar states of a special type of monomials which we define as standard monomials. Then, we provide an algorithm to explicitly compute the Haar states of standard monomials on $O (S L_{q} (3))$ with reasonable computational cost. The numerical results on $O (S L_{q} (3))$ will be used in the future study of the $q$ -deformed Weingarten function.

Update the introduction section. Add a new section (Section 3). Add more details on the computation of the Source Matrix (Section 4.1) and the recursive relation of standard monomial in the form of (cdh)^i(ceg)^{m-i} (section 4.2). Remove appendix A and B in the previous version

Computing the Haar state on O(SLq​(3))

Abstract

Computing the Haar state on $O (S L_{q} (3))$