Level-one Highest Weight Representation of $U_q[\hat{sl(N|1)}]$ and Bosonization of the Multi-component Super t-J Model

TL;DR

This paper explores the structure of certain quantum affine superalgebra representations, computes their characters, and constructs bosonized vertex operators to model the multi-component super t-J system.

Contribution

It provides a new bosonization framework for the level-one irreducible highest weight representations of $U_q[\hat{sl(N|1)}]$ and applies it to the super t-J model.

Findings

Derived explicit characters and supercharacters.

Constructed bosonized q-vertex operators and established their exchange relations.

Bosonized the multi-component super t-J model using these operators.

Abstract

We study the level-one irreducible highest weight representations of the quantum affine superalgebra $U_q[\hat{sl(N|1)}]$, and calculate their characters and supercharacters. We obtain bosonized q-vertex operators acting on the irreducible $U_q[\hat{sl(N|1)}]$-modules and derive the exchange relations satisfied by the vertex operators. We give the bosonization of the multi-component super $t-J$ model by using the bosonized vertex operators.