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A.A.Belavin, A.V.Odesskii, R.A.Usmanov

Landau Institute for Theoretical Physics, Chernogolovka, Moscow region, 142432, Russia

New relations in the algebra of the Baxter Q-operators

We consider irreducible cyclic representations of the algebra of monodromy matrices correseponding to the R-matrix of the six-vertex model. In roots of unity the Baxter Q-operator can be represented as a trace of a tensor product of L-operators appropriate to one of such representations. It satisfies the TQ-equation. We find a new algebraic structure generating by these L-operators, and as consequence, by the Q-operators.