Multiparameter Deformations of the Algebra $gl_n$ in Terms of Anyonic Oscillators

Abstract

Generators of multiparameter deformations $U_{q;s_1,s_2,...,s_{n-1}}(gl_n)$ of the universal enveloping algebra $U(gl_n)$ are realized bilinearly by means of appropriately generalized form of anyonic oscillators (AOs). This modification takes into account the parameters $s_1,...,s_{n-1}$ and yields usual AOs when all the $s_i$ are set equal to unity.