Matrix valued orthogonal polynomials and quantum groups
Noud Aldenhoven · Radboud Repository (Radboud University) · 2016
In my second year as a Ph.D. student I read about the distinction between two archetypes of mathematicians, which Freeman Dyson called birds and frogs.Birds fly high up in the air and have a great overview of mathematics.Frogs live in the mud, are blind to the great overview, but spot many precious and beautiful stones and pearls that the birds have missed.I quote the paper of Dyson [37].Some mathematicians are birds, others are frogs.Birds fly high in the air and survey broad vistas of mathematics out to the far horizon.They delight in concepts that unify our thinking and bring together diverse problems from different parts of landscape.Frogs live in the mud below and see only the flowers that grow nearby.They delight in the details of particular objects, and they solve problems one at a time.This thesis is written by a frog who spent four years in a muddy field.If this thesis is opened on an arbitrary page one might think that this thesis contains mud and mud only.Fortunately this is not the case.For four years I have been exploring the muddy field of special functions in relation to the representations theory of quantum symmetric pairs.With the help of my supervisors and many other helpful mathematicians I came across many precious and beautiful stones and pearls, like Dyson's frogs, which I tried to unify in this thesis.If you want see the same precious and beautiful stones and pearls which I found, you have to get your hands dirty and slog with me through the mud.