Quantum Groups GLp,q(2)- and SUq(1)/q(2)(2)-Invariant Bosonic Gases: A Comparative Study

We discuss the algebras, representations, and thermodynamics of quantum group bosonic gas models with two different symmetries: GLp,q(2) and SUq(1)/q(2)(2). We establish the nature of the basic numbers which follow from these GLp,q(2)- and SUq(1)/q(2)(2)-invariant bosonic algebras. The Fock space representations of both of these quantum group invariant bosonic oscillator algebras are analyzed. It is concisely shown that these two quantum group invariant bosonic particle gases have different algebraic and high-temperature thermo-statistical properties.