Quantum Toda chains intertwined

Abstract:

An explicit construction of integral operators intertwining various quantum Toda chains is conjectured. Compositions of the intertwining operators provide recursive and $\mathcal {Q}$-operators for quantum Toda chains. In particular the authors’ earlier results on Toda chains corresponding to classical Lie algebras are extended to the generic $BC_n$- and Inozemtsev–Toda chains. Also, an explicit form of $\mathcal {Q}$-operators is conjectured for the closed Toda chains corresponding to the Lie algebras $B_{\infty }$, $C_{\infty }$, $D_{\infty }$, the 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.