In my research, I study a class of special functions, the Macdonald-Koornwinder (MK) polynomials, and their relations to quasi-geometric objects called quantum symmetric pairs. In the first part of my dissertation, I generalise the MK polynomials to the so-called Intermediate Macdonald Polynomials and prove some of their properties. In the second part, I develop tools further tools to study the rank-1 MK polynomials, namely the non-symmetric shift operators. In the third part, I formulate a general theory and general methods for obtaining special functions from quantum symmetric pairs, summarise some of the literature of how to obtain MK polynomials, and then show that in some more general cases we can obtain intermediate Macdonald polynomials.
Philip Schlösser was born in Munich, Germany, went to school in Dresden and Munich, and got their Abitur in 2016. They went to study physics at the University of Konstanz from 2016 until 2019. They followed their bachelor's degree up with a double master's in maths and theoretical physics from the University of Amsterdam in 2022. Philip has been doing their PhD at Radboud University ever since.