Pieri rules, vertex operators and Baxter Q-matrix

Antoine Duval (1) , Vincent Pasquier (2)

1 University of Texas at El Paso (UTEP) - Department of Mathematical Sciences
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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 $\omega$-duality transformation. We observe that the scalar product of two higher spin XXZ wave functions can be expressed with a Gaudin determinant.

Domains: Mathematical Physics [math-ph]

Antoine Duval, Vincent Pasquier. Pieri rules, vertex operators and Baxter Q-matrix. 2019. ⟨cea-01231805⟩