Q-Boson Representation of the Quantum Matrix Algebra $M_q(3)$

TL;DR

This paper constructs an infinite dimensional q-boson representation of the quantum matrix algebra $M_q(3)$, enabling realization of $GL_q(3)$, thus advancing the understanding of quantum group representations.

Contribution

It introduces the first infinite dimensional q-boson representation of $M_q(3)$ and uses it to realize $GL_q(3)$, filling a gap in quantum matrix algebra representations.

Findings

Constructed an infinite dimensional representation of $M_q(3)$

Realized $GL_q(3)$ using q-bosons

Provides a new tool for quantum group representation theory

Abstract

{Although q-oscillators have been used extensively for realization of quantum universal enveloping algebras,such realization do not exist for quantum matrix algebras ( deformation of the algebra of functions on the group ). In this paper we first construct an infinite dimensional representation of the quantum matrix algebra $ M_q ( 3 ) $(the coordinate ring of $ GL_q (3)) $ and then use this representation to realize $ GL_q ( 3 ) $ by q-bosons.}