Quantum permanents and Hafnians via Pfaffians
Quantum Algebra
2016-08-30 v2 Mathematical Physics
Combinatorics
math.MP
Rings and Algebras
Abstract
Quantum determinants and Pfaffians or permanents and Hafnians are introduced on the two parameter quantum general linear group. Fundamental identities among quantum Pf, Hf, and det are proved in the general setting. We show that there are two special quantum algebras among the quantum groups, where the quantum Pfaffians have integral Laurent polynomials as coefficients. As a consequence, the quantum Hafnian is computed by a closely related quantum permanent and identical to the quantum Pfaffian on this special quantum algebra.
Keywords
Cite
@article{arxiv.1504.01538,
title = {Quantum permanents and Hafnians via Pfaffians},
author = {Naihuan Jing and Jian Zhang},
journal= {arXiv preprint arXiv:1504.01538},
year = {2016}
}
Comments
12 pages. Final expanded version with new title. Results are upgraded to 2-parameter cases