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.
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Supported by NSFC (Grant Nos. 11271138 and 11531004), Simons Foundation (Grant 198129) and a CSC fellowship.
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Jing, N., Zhang, J. Quantum Permanents and Hafnians via Pfaffians. Lett Math Phys 106, 1451–1464 (2016). https://doi.org/10.1007/s11005-016-0881-3
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DOI: https://doi.org/10.1007/s11005-016-0881-3