Haglund’s conjecture and Clebsch-Gordan rule for Macdonald polynomials [HBNI Th241]

Abstract

This thesis is divided in two parts. The rst part is about a conjecture of J. Haglund on expansion of the (normalized) integral form Macdonald symmetric functions in terms of the Schur basis. The second part of the thesis concerns the product of type SL2 Macdonald polynomials. This part is based on a joint work with Arun Ram.