A multivariate analogue of Ruijsenaars's generalised hypergeometric function

A quantum algebra approach

Master thesis (2023)

Authors

R.M. Ledoux Electrical Engineering, Mathematics and Computer Science

Contributors

W.G.M. Groenevelt Analysis - EEMCS (supervisor 1)
J.M.A.M. van Neerven Analysis - EEMCS (supervisor 2)
F.M. de Oliveira Filho Discrete Mathematics and Optimization - EEMCS (supervisor 2)
Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright: © 2023 Rik Ledoux
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Published Date

30-08-2023

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

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/.