Rikard Bögvad: A problem on Gelfand models and rings of differential operators for (some) reflection groups
Time: Tue 2016-02-16 13.00
Location: Room 34, building 5, Kräftriket, Department of mathematics, Stockholm university
Participating: Rikard Bögvad, Stockholm university
A Gelfand model of a group is a representation that contains one copy of each irreducible representation. It is a problem to construct it in a natural way, for example for reflection groups. Starting with a finite group G with a complex representation V, one may try the following construction: take the polynomial algebra S(V), the ring of differential operators D on S(V), and consider the vector space W in S(V) that is
annihilated by D^G_-, the invariant differential operators of negative degree. We have shown that if a certain ring R is commutative then W gives a Gelfand model, and also that R is commutative for certain reflection groups, e.g. symmetric and generalized symmetric groups. One may ask for which general reflection groups G(de,e,n) that R ---which is very concretely given---is commutative.
One does not need to understand any of the above(except possibly commutative, ring and group….) to understand the problem.
A reference is Bøgvad/Kallström arXiv:1506.06229.