SIGMA 22 (2026), 105, 65 pages      arXiv:2604.21785      https://doi.org/10.3842/SIGMA.2026.105

Orthosymplectic Quantum Groups Revisited

Kyungtak Hong and Alexander Tsymbaliuk
Purdue University, Department of Mathematics, West Lafayette, IN 47907, USA

Received April 29, 2026, in final form October 05, 2026; Published online October 30, 2026

Abstract
We present the RLL-realization of extended orthosymplectic quantum supergroups for any parity sequence, with $R$-matrices evaluated in the earlier work [Lett. Math. Phys. 116 (2026), 55, 97 pages, arXiv:2408.16720]. Our isomorphism is compatible with the internal structure of generalized doubles. We also relate different sign conventions through 2-cocycle twists.

Key words: double; $R$-matrix; orthosymplectic; 2-cocycle twist; RLL-realization; quantum group.

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