Boxed Skew Plane Partition and Integrable Phase Model

TL;DR

This paper explores the connection between boxed skew plane partitions and the integrable phase model, deriving determinant formulas for generalized scalar products and linking them to generating functions of these partitions.

Contribution

It introduces a generalized scalar product for the phase model and demonstrates its relation to skew Schur functions and plane partition generating functions.

Findings

Scalar product expressed as a determinant in two different ways

Connection established between scalar products and generating functions of plane partitions

Generalized scalar product linked to spectral parameters of the phase model

Abstract

We study the relation between the boxed skew plane partition and the integrable phase model. We introduce a generalization of a scalar product of the phase model and calculate it in two ways; the first one in terms of the skew Schur functions, and another one by use of the commutation relations of operators. In both cases, a generalized scalar product is expressed as a determinant. We show that a special choice of the spectral parameters of a generalized scalar product gives the generating function of the boxed skew plane partition.