Coupled Hall-Littlewood functions, vertex operators and the $q$-boson model

TL;DR

This paper introduces coupled Hall-Littlewood functions, constructs their vertex operator realization, and applies these to represent the two-site $q$-boson model and compute the topological string partition function.

Contribution

It defines coupled Hall-Littlewood functions, develops their vertex operator realization, and links them to the $q$-boson model and topological string theory.

Findings

Representation of the $q$-boson model using coupled Hall-Littlewood functions

Vertex operators generate coupled Hall-Littlewood functions

Partition function of the A-model topological string on the conifold derived

Abstract

In this paper, we firstly give the definition of the coupled Hall-Littlewood function and its realization in terms of vertex operators. Then we construct the representation of the two-site generalized $q$-boson model in the algebra of coupled Hall-Littlewood functions. Finally, we find that the vertex operators which generate coupled Hall-Littlewood functions can also be used to obtain the partition function of the A-model topological string on the conifold.