# Binomial formulas for Macdonald polynomials

Binomial formulas for Macdonald polynomials

Authorvan den Boom, Eddo (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Analysis)

Groenevelt, Wolter (mentor)

van Neerven, Jan (graduation committee)

Gijswijt, Dion (graduation committee)

Delft University of Technology

Programme Date2019-03-22

AbstractSymmetric and nonsymmetric Macdonald polynomials associated to root systems are very general families of orthogonal polynomials in multiple variables. Their definition is quite complex, but in certain cases one can define so-called interpolation polynomials that have a surprisingly simple definition and are related to the Macdonald polynomials by a binomial formula. In this thesis we will discuss such formulas for two kinds of root systems: type A and type (C∨,C). For the latter case, there are still some open questions that remain unanswered.

SubjectMacdonald polynomials

Binomial formula

Interpolation polynomials

Affine Hecke algebra

Koornwinder polynomials

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Part of collectionStudent theses

Document typemaster thesis

Rights© 2019 Eddo van den Boom