Harmonic analysis on vector bundles over compact symmetric spaces.

Maarten van Pruijssen (Paderborn University)

Tuesday 28th March, 2017 16:00-17:00 Maths 203


Harmonic analysis on the trivial line bundle over a compact symmetric space U/K is well understood. The space of K-invariant sections can be described by families of orthogonal polynomials with nice properties. For example, the polynomials are simultaneous eigenfunctions of a commutative algebra of differential operators. This shows that the polynomials are actually hypergeometric functions.

Much of this classical analysis can also be performed on more general vector bundles over compact symmetric spaces. The condition under which this works out nicely is "multiplicity free induction of the K-type".

I will discuss the classical theory and indicate how to generalize the involved constructions under the multiplicity freeness condition. I will briefly discuss a classification of data that provides an abundance of multiplicity free K-types. Finally I will present explicit examples of families of vector valued orthogonal polynomials in several variables with properties similar to that of families of Jacobi polynomials.

My talk will be based on joint work with Erik Koelink (Nijmegen, NL) and Pablo Roman (Cordoba, Arg).

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