Multivariate generalisations of classical hypergeometric polynomials from Lie theory

In this thesis, we will be studying Lie groups and their connection to certain orthogonal polynomials. We will look into the classical Krawtchouk, Meixner and Laguerre polynomials, and the multivariate Krawtchouk and Meixner polynomials as defined by Iliev. Using representations of the Lie groups SU(2) and SU(1,1), it will be shown that the...

Een analytische en algebraïsche beschouwing van de Wilson- en Racahpolynomen

De Wilson- en Racahpolynomen zijn hypergeometrische orthogonale polynomen die helemaal bovenaan staan in het Askey-schema. Deze polynomen zijn de meest algemene hypergeometrische orthogonale polynomen in één variabele en generaliseren de andere hypergeometrische orthogonale polynomen in het Askey-schema.<br/><br/>In deze scriptie wordt ingegaan...

Representation theory and the regular representation: Splitting the regular representation into its group invariant subspaces

Representation theory is a branch in mathematics that studies group homomorphisms between a group and the automorphism group of a vector space. A special representation that every group has is the regular representation. This representation permutes all elements of the group in a vector space which dimension is equal to the order of the group....