Representations and Q-Boson Realization of the Algebra of Functions on the Quantum Group GLq(N)

TL;DR

This paper explores the representations of the algebra of functions on the quantum group GL_q(N), introduces a q-analogue of the root system, and provides explicit matrix and q-boson realizations of its generators.

Contribution

It introduces a q-analogue of the root system for GL_q(N) and constructs explicit matrix and q-boson realizations of its algebra generators.

Findings

Constructed a q-analogue of the root system for GL_q(N)

Derived explicit matrix representations of the algebra generators

Provided a q-boson realization of the generators

Abstract

We present a detailed study of the representations of the algebra of functions on the quantum group $ GL_q(n) $. A q-analouge of the root system is constructed for this algebra which is then used to determine explicit matrix representations of the generators of this algebra. At the end a q-boson realization of the generators of $ GL_q(n) $ is given.