$Q$-Operator and the Drinfeld Equation

A. A. Belavin, R. A. Usmanov

L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: We show that the $TQ$ equation is satisfied by the trace over the quantum space of the product of $R$-matrices intertwining two representations of the quantum double of the Borel subalgebra of the affine algebra $U_{\text{q}}(\widehat{sl}_2)$ (the standard two-dimensional and the $N$-dimensional cyclic representations).

Keywords: quantum groups, Baxter $Q$-operator, cyclic representations.

DOI: 10.4213/tmf195

 English version: Theoretical and Mathematical Physics, 2003, 135:3, 757–764

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