English

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

Quantum Algebra 2024-04-24 v3 Probability

Abstract

This paper shows that to compute the Haar state on O(SLq(n))\mathbb{O}(SL_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(SLq(3))\mathbb{O}(SL_q(3)) with reasonable computational cost. The numerical results on O(SLq(3))\mathbb{O}(SL_q(3)) will be used in the future study of the qq-deformed Weingarten function.

Cite

@article{arxiv.2301.12683,
  title  = {Computing the Haar state on ${\mathbb{O}(SL_q(3))}$},
  author = {Ting Lu},
  journal= {arXiv preprint arXiv:2301.12683},
  year   = {2024}
}

Comments

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

R2 v1 2026-06-28T08:26:02.193Z