Infinite Families of Gauge-Equivalent $R$-Matrices and Gradations of Quantized Affine Algebras

Details Infinite Families of Gauge-Equivalent $R$-Matrices and Gradations of Quantized Affine Algebras Infinite Families of Gauge-Equivalent $R$-Matrices and Gradations of Quantized Affine Algebras

1993-10-28

arxiv.org/abs/hep-th/9310183v6

Int.J.Mod.Phys.B8:3679-3691,1994

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, Latex, UQMATH-93-10 (final version for publication)

Scientific paper

10.1142/S0217979294001585

Associated with the fundamental representation of a quantum algebra such as $U_q(A_1)$ or $U_q(A_2)$, there exist infinitely many gauge-equivalent $R$-matrices with different spectral-parameter dependences. It is shown how these can be obtained by examining the infinitely many possible gradations of the corresponding quantum affine algebras, such as $U_q(A_1^{(1)})$ and $U_q(A_2^{(1)})$, and explicit formulae are obtained for those two cases. Spectral-dependent similarity (gauge) transformations relate the $R$-matrices in different gradations. Nevertheless, the choice of gradation can be physically significant, as is illustrated in the case of quantum affine Toda field theories.

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