Orthosymplectic quantum groups revisited
Kyungtak Hong, Alexander Tsymbaliuk
TLDR
This paper presents the RLL-realization of orthosymplectic quantum supergroups, compatible with generalized doubles, and factorizes the R-matrix.
Key contributions
- Presents RLL-realization of extended orthosymplectic quantum supergroups for any parity sequence.
- Demonstrates isomorphism compatibility with the internal structure of generalized doubles.
- Relates different sign conventions using 2-cocycle twists.
- Establishes factorization of the reduced R-matrix within the RLL-realization.
Why it matters
This paper significantly advances the understanding of orthosymplectic quantum supergroups by introducing a novel RLL-realization. It clarifies their internal structure and R-matrix properties, which is crucial for theoretical physics and mathematical frameworks.
Original 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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