Inhomogenous model of crossing loops and multidegrees of some algebraic varieties

TL;DR

This paper studies an inhomogeneous quantum integrable model linked to the Brauer algebra, analyzing its ground state eigenvector and revealing connections to algebraic varieties' multidegrees.

Contribution

It introduces a novel inhomogeneous model based on the Brauer algebra and explores its ground state properties and algebraic geometric connections.

Findings

Derived sum rules for the ground state eigenvector.

Linked entries of the eigenvector to multidegrees of algebraic varieties.

Provided insights into the structure of the model and its mathematical properties.

Abstract

We consider a quantum integrable inhomogeneous model based on the Brauer algebra B(1) and discuss the properties of its ground state eigenvector. In particular we derive various sum rules, and show how some of its entries are related to multidegrees of algebraic varieties.