Binomial formulas for Macdonald polynomials

Master thesis (2019)

Authors

E.P.G. van den Boom Electrical Engineering, Mathematics and Computer Science

Contributors

W.G.M. Groenevelt Analysis - EEMCS (mentor)
J.M.A.M. van Neerven Analysis - EEMCS (graduation committee member)
Dion Gijswijt Discrete Mathematics and Optimization - EEMCS (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2019 Eddo van den Boom
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Published Date

22-03-2019

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

Symmetric 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.