✍ Scribed by R. Floreanini; L. Vinet
No coin nor oath required. For personal study only.
A quantum-algebraic framework for many (q)-special functions is provided. The twodimensional Euclidean quantum algebra, (s l_{4}(2)) and the (q)-oscillator algebra are considered. Realizations of these algebras in terms of operators acting on vector spaces of functions in one complex variable are given. Basic hypergeometric functions are shown to arise, in analogy with Lie theory, as matrix elements of certain operators. New generating functions for these 4 -special functions are obtained. 1993 Academic Press. Inc.
📜 SIMILAR VOLUMES
We studied asymptotic methods for \(q\)-Schur algebras and related quantum groups and constructed a kind of asymptotic form for \(q\)-Schur algebras and quantum special linear groups. The structure and representations for these forms were also discussed. (6) 1995 Academic Press, Inc.
The discussions in the present paper arise from exploring intrinsically the structural nature of the quantum n-space. A kind of braided category of -graded θcommutative associative algebras over a field k is established. The quantum divided power algebra over k related to the quantum n-space is intr
Using Darboux transformations for the lattice Schrödinger equation, we construct two families of discrete reflectionless potentials with \(j\) and \(2 j\) bound states (solitons). These potentials are related to the exceptional Askey-Wilson polynomials. In the continuous limit they are reduced to th
Constructions are described which associate algebras to arbitrary bilinear forms, generalising the usual Clifford and Heisenberg algebras. Quantum groups of symmetries are discussed, both as deformed enveloping algebras and as quantised function spaces. A classification of the equivalence classes of