Partition Identities, Presburger Constructibility and Satake inversion

Time: 9:00 - 10:00, 8th June

Venue: Room 507, A6, Institute of Mathematics

Abstract: The Presburger constructible functions are those elements in the ring of constructible motivic functions (in the sense of Cluckers-Loeser) that are built from data given by the Presburger language in Z (the value group sort) and the functions and constants involving the formal symbol L. We show some results around the Presburger constructibility of certain partition functions of positive integers. Using results of Hahn et al. we show that the explicit Satake inversion that they obtain using a combinatorial approach from partition identities, can be also obtained in the ring of constructible motivic functions. We formulate questions about possible generalizations. This is a work in progress