Pieri rules, vertex operators and Baxter Q-matrix

Abstract

We use the Pieri rules to recover the q-boson model and show it is equivalent to a discretized version of the relativistic Toda chain. We identify its semi infinite transfer matrix and the corresponding Baxter Q-matrix with half vertex operators related by an ω-duality transformation. We observe that the scalar product of two higher spin XXZ wave functions can be expressed with a Gaudin determinant.

misprints corrected. An example added

References in corpus (3)

• Gaudin functions, and Euler-Poincaré characteristics
• From Quantum Bäcklund Transforms to Topological Quantum Field Theory
• Adding \pm 1 to the argument of an Hall-Littlewood polynomial

Cited by in corpus (4)

• The open XXX spin chain in the SoV framework: scalar product of separate states
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• All correlation functions of the open XXX spin 1/2 quantum chains for unparallel boundary magnetic fields with one constraint