The denominators of normalized \(R\)-matrices of types \(A_{2n-1}^{(2)}\), \(A_{2n}^{(2)}\), \(B_{n}^{(1)}\) and \(D_{n+1}^{(2)}\).(English)Zbl 1337.81080
The denominators of normalized \(R\)-matrices play an important role in studying finite-dimensional integrable representations and have been investigated by a number of authors. In this paper under review, by following the ideas from [T. Akasaka andM. Kashiwara, Publ. Res. Inst. Math. Sci. 33, No. 5, 839–867 (1997;Zbl 0915.17011)] and [S.-J. Kang et al., Duke Math. J. 164, No. 8, 1549–1602 (2015;Zbl 1323.81046)], the author provides a general framework for calculating the denominators of all normalized \(R\)-matrices of types \(A^{(2)}_{2n-1}(n\geq 3)\), \(A^{(2)}_{2n}(n\geq 2)\), \(B^{(1)}_{n}(n\geq 3)\) and \(D^{(2)}_{n+1}(n\geq 2)\). Then the denominator formulas are explicitly given. It is concluded that the normalized \(R\)-matrices of types \(A^{(2)}_{2n-1}(n\geq 3)\), \(A^{(2)}_{2n}(n\geq 2)\), \(B^{(1)}_{n}(n\geq 3)\) and \(D^{(2)}_{3}\) have only simple poles, and under some additional conditions, those of types \(D^{(2)}_{n+1}(n\geq 3)\) have double poles.
Reviewer: Ming Ding (Tianjin)
MSC:
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 16T25 | Yang-Baxter equations |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
Cite
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