A multivariate analogue of Ruijsenaars's generalised hypergeometric function

A multivariate analogue of Ruijsenaars's generalised hypergeometric function: A quantum algebra approach

Ledoux, Rik (TU Delft Electrical Engineering, Mathematics and Computer Science)

Groenevelt, W.G.M. (mentor)
van Neerven, J.M.A.M. (graduation committee)
de Oliveira Filho, F.M. (graduation committee)

Delft University of Technology

Applied Mathematics

2023-08-30

In this thesis, we derive a multivariate analogue of Ruijsenaars’s 2F1-generalisation R. We use Hopf algebra representation theory of the modular double of sl.2/, a Hopf algebra structure strongly related to quantum groups, to relate the function R to overlap coefficients of eigenfunctions. Using properties of the algebra and the representation, we derive an Askey-Wilson type difference equation. We moreover recover Ruijsenaars’s unitary transformation kernel E.

Expanding on the Hopf algebra structure, we extend our derivations to the multivariate version of R. Employing representation theory, we obtain multivariate difference equations. Furthermore, we demonstrate that the multivariate function enables the definition of a unitary transformation on multivariate functions in L2..0; ∞/N/.

quantum groups
Representation Theory
mathematical physics

http://resolver.tudelft.nl/uuid:00b69a76-b3d4-49b6-be0f-f31307b51db9

Student theses

master thesis

© 2023 Rik Ledoux