Multiparameter Deformations of the Algebra $g{l}_n$ in Terms of Anyonic Oscillators

Abstract

Generators of multiparameter deformations $U_{q;s_1,s_2,...,s_{n-1}}(g{l}_n)$ of the universal enveloping algebra $U(g{l}_n)$ 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.

7 pages, Latex, no figures (Talk given at the Conference "Symmetry in Nonlinear Mathematical Physics", Kiev, July 1995)

References in corpus (5)

• Anyons and Quantum Groups
• Generalized Quon Statistics
• Anyonic Realization of $S{U}_q(N)$ Quantum Algebra
• $q$-Deformed Classical Lie Algebras and their Anyonic Realization
• Anyonic Construction of the $S{L}_{Q,s}(2)$ Algebra