BC Toda chain II: symmetries. Dual picture

Abstract

In the previous paper we derived Gauss-Givental integral representation for the wave functions of quantum BC Toda chain and also introduced Baxter operators for this model. In the present paper we prove commutativity of Baxter operators, as well as show that the constructed wave functions are symmetric with respect to signed permutations of spectral parameters and diagonalize Baxter operators. Furthermore, we derive Mellin-Barnes integral representation for the wave functions. With its help we show that wave functions satisfy dual system of difference equations with respect to spectral parameters and coincide with hyperoctahedral Whittaker functions. Finally, we give heuristic proofs of orthogonality and completeness of the wave functions.

Figures (28)

• Figure 1: Elements of diagrams
• Figure 2: "Ghosts"
• Figure 3: Bold vertices depict integration
• Figure 4: Star-triangle relations
• Figure 5: Chain relations

Theorems & Definitions (65)

• Example 1
• Remark 1
• Theorem \ref{thm:Psi-sym}
• Theorem \ref{theorem2.2}
• Proposition \ref{prop:gl-bc-prod}
• Theorem \ref{theorem2.3}
• Example 2
• Corollary \ref{cor:Psi-an}
• Theorem \ref{theoremMB4}
• Proposition \ref{propK2}