Boxed UC plane partitions and the two-site generalized phase model

TL;DR

This paper explores the relationship between boxed UC plane partitions and a two-site generalized phase model, establishing a generating function expressed through Schur functions and connecting it to UC plane partitions with a double scaling limit.

Contribution

It introduces two maps to connect boxed UC plane partitions with the two-site generalized phase model and derives a generating function in terms of Schur functions.

Findings

Generated function expressed as products of Schur functions

Connection established between boxed UC plane partitions and the phase model

Link to UC plane partitions with double scaling limit

Abstract

This study investigates the connection between boxed UC plane partitions and the two-site generalized phase model. By introducing two maps, we investigate the representation of two-side generalized phase algebras and actions of monodromy matrix operators on basis vectors. The generating function of boxed UC plane partitions is established by the scalar product of the two-site generalized phase model, which can be expressed as products of Schur functions. It is shown that the generating function of boxed UC plane partitions is that of UC plane partitions with the double scaling limit.