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 algebra 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.
Keywords:quantum Toda Hamiltonians, elementary intertwining operator, recursive operator, quantization Pasquier–Gaudin integral $Q$-operator.
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