Quantum Toda Chains Intertwined

Abstract

We conjecture an explicit construction of integral operators intertwining various quantum Toda chains. Compositions of the intertwining operators provide recursive and Q-operators for quantum Toda chains. In particular we propose a generalization of our previous results for Toda chains corresponding to classical Lie algebra to the generic BC_n and Inozemtsev Toda chains. We also conjecture explicit form of Q-operators for closed Toda chains corresponding to Lie algebras B_{\infty}, C_{\infty}, D_{\infty}, affine Lie algebras B^{(1)}_n, C^{(1)}_n, D^{(1)}_n, D^{(2)}_n, A^{(2)}_{2n-1}, A^{(2)}_{2n} and the affine analogs of BC_n and Inozemtsev Toda chains.