Abstract. The key point of the Hamiltonian formalism of Toda molecules is the commutativity of the Hamiltonians (tr y^k, tr y^l)=0, where y in GL(n) and (,) is a Poisson bracket associated with the classical r-matrix. To quantize the Toda molecule, we have to consider the q-analogue of the above formula. In this paper, we show the commutativity of the quantized first- and higher-order Hamiltonians (tr_q X^m, tr_q X)=0, where X is a matrix of quantum group GL_q(n).

Print publication: Issue 17 (7 September 1994)