The q-Boson Realizations of the Quantum Group $U_{q}(sl(n+1,C))$

TL;DR

This paper provides explicit recursive formulas for realizing the quantum group $U_q(sl(n+1,C))$ using q-boson pairs, enhancing the algebra's explicit representations for mathematical and physical applications.

Contribution

It introduces new recursive formulas for the canonical realization of $U_q(sl(n+1,C))$ using q-boson pairs and an auxiliary $U_q(gl(n,C))$ representation.

Findings

Explicit recursive formulas for generators

Representation using q-boson pairs

Connection to $U_q(gl(n,C))$ auxiliary representation

Abstract

We give explicit expression of recurrency formulae of canonical realization for quantum enveloping algebras $U_{q}(sl(n+1,C))$. In these formulas the generators of the algebra $U_{q}(sl(n+1,C))$ are expressed by means of n-canonical q-boson pairs one auxiliary representation of the algebra $U_{q}(gl(n,C))$.