Extension of the vector-representation identification to twisted face weights

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Let g{\bf g} be one of the twisted affine Lie algebra types A2n(2)A_{2n}^{(2)} or A2n−1(2)A_{2n-1}^{(2)}, or let the type be G2(1)G_2^{(1)}. Let R(λ){\cal R}(\lambda) denote the universal dynamical RR matrix, and let the corresponding face-type elliptic solutions be Kuniba's solutions for A2n(2)A_{2n}^{(2)} and A2n−1(2)A_{2n-1}^{(2)}, and Kuniba–Suzuki's solution for G2(1)G_2^{(1)}. Twisted vector-representation conjecture. A statement analogous to the theorem identifying the vector representation of R(λ){\cal R}(\lambda) with Jimbo–Miwa–Okado's elliptic solutions is true for Kuniba's solutions of types A2n(2)A_{2n}^{(2)} and A2n−1(2)A_{2n-1}^{(2)}, and for Kuniba–Suzuki's solution of type G2(1)G_2^{(1)}. The claim is motivated by the common 2×22\times2 block structure of the relevant RR matrices, but the supplied text gives no proof or resolution.

References

Primary source

Hitoshi Konno, “Dynamical R Matrices of Elliptic Quantum Groups and Connection Matrices for the q-KZ Equations”, arXiv:math/0612558 (2006).

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