Coherent States of gl q ( 2 ) - covariant Oscillators

In this paper two types of coherent states of gl q (2)-covariant oscil-lators are investigated. 1 Quantum groups or q-deformed Lie algebra implies some specific deformations of classical Lie algebras. From a mathematical point of view, it is a non-commutative associative Hopf algebra. The structure and representation theory of quantum groups have been developed extensively by Jimbo [1] and Drinfeld [2]. The q-deformation of Heisenberg algebra was made by Arik and Coon [3], Macfarlane [4] and Biedenharn [5]. Recently there has been some interest in more general deformations involving an arbitrary real functions of weight generators and including q-deformed algebras as a special case [6-10]. Recently V.Spiridonov [11] found the new coherent states of the q-Weyl algebra aa † − qa † a = 1, 0 < q < 1 which are defined as eigenstates of the operator a † .