A correction factor for Kac-Moody groups and t-deformed root multiplicities
Infinite dimensional analogues of classical formulas from the theory of p-adic groups give rise to a certain correction factor. For example, Macdonald's formula for the spherical function and the Casselman-Shalika formula, when extended to the affine, and general Kac-Moody setting, all have this feature.
We will discuss this correction factor. In affine type, it is known by Cherednik's work on Macdonald's constant term conjecture. More generally, it can be represented as a collection of polynomials of t indexed by positive imaginary roots; these are deformations of root multiplicities. Methods of computing imaginary root multiplicities, such as the Peterson algorithm and the Berman-Moody formula can be generalized to compute the correction factor for any t. They both reveal some properties of the correction factor and raise further questions and conjectures about its structure. This is joint work with Dinakar Muthiah and Ian Whitehead.
Write me (email@example.com) if you want to be added to the mailing list of the seminar and get announcements and Zoom links for upcoming talks.