Orthosymplectic quantum groups revisited
Kyungtak Hong, Alexander Tsymbaliuk
TL;DR
This paper revisits orthosymplectic quantum supergroups, providing a new RLL-realization compatible with their internal structure, and relates sign conventions via 2-cocycle twists, including a factorization of the reduced R-matrix.
Contribution
It introduces a novel RLL-realization for extended orthosymplectic quantum supergroups for any parity sequence, enhancing understanding of their algebraic structure.
Findings
Established an isomorphism compatible with generalized doubles
Related sign conventions through 2-cocycle twists
Factorized the reduced R-matrix within the RLL-realization
Abstract
We present the RLL-realization of extended orthosymplectic quantum supergroups for any parity sequence, with R-matrices evaluated in the earlier work arxiv:2408.16720. Our isomorphism is compatible with the internal structure of generalized doubles. We also relate different sign conventions through 2-cocycle twists. Furthermore, we establish a factorization of the reduced R-matrix within the RLL-realization.
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