q-Deformed orthogonal and pseudo-orthogonal algebras and their representations

q-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations

Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebras and root vectors and which make it possible to construct representations by operators acting according to Gel’fand–Tsetlin-type formulas. Unitary representations of the q-deformed algebras Uq(son,1) are found. AMS subject classifications (1980). 16...

q-Deformed Inhomogeneous Algebras Uq(ison) and Their Representations

Proceeding from the nonstandard q-deformed algebras U ′ q(son+1) and their finitedimensional representations in a q-analog of the Gel’fand-Tsetlin basis, we obtain, by means of the contraction procedure, the corresponding q-deformed inhomogeneous algebras U ′ q(ison) in a uniform fashion for all n ≥ 2 as well as their infinite-dimensional representations.

ITP-97-8E q-alg/9709036 q-DEFORMED ALGEBRAS Uq(son) AND THEIR REPRESENTATIONS

Monomiality, Orthogonal and Pseudo-orthogonal Polynomials

We reconsider some families of orthogonal polynomials, within the framework of the so called monomiality principle. We show that the associated operational formalism allows the framing of the polynomial orthogonality using an algebraic point of view. Within such a framework, we introduce families of pseudo-orthogonal polynomials, namely polynomials, not orthogonal under the ordinary definition,...

q-deformed W-algebras and elliptic algebras

The elliptic algebra Aq,p(ŝl(N)c) at the critical level c = −N has an extended center containing trace-like operators t(z). Families of Poisson structures, defining q-deformations of the WN algebra, are constructed. The operators t(z) also close an exchange algebra when (−p1/2)NM = q−c−N for M ∈ Z. It becomes Abelian when in addition p = qNh where h is a non-zero integer. The Poisson structures...