Gauss hypergeometric function and quadratic $R$-matrix algebras

Abstract

We consider representations of quadratic $R$-matrix algebras by means of certain first order ordinary differential operators. These operators turn out to act as parameter shifting operators on the Gauss hypergeometric function and its limit cases and on classical orthogonal polynomials. The relationship with W. Miller's treatment of Lie algebras of first order differential operators will be discussed.

26 pages

References in corpus (1)

• Quantum Inverse Scattering Method. Selected Topics

Cited by in corpus (6)

• Baxter Q-Operators and Representations of Yangians
• Representations of reflection algebras
• A q-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra
• Gauss hypergeometric function and quadratic R-matrix algebras
• Kowalevski top revisited
• Vadim Kuznetsov. Informal Biography by Eyes of His First Adviser