Uniformity in representation theory
Connections for Women: Model Theory and Its Interactions with Number Theory and Arithmetic Geometry February 10, 2014 - February 11, 2014
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC Secondary Mathematics Subject Classification No Secondary AMS MSC
Fix an integer n and prime number p>>n. The compact groups
SL_n(Z_p) and SL_n(F_p[[t]]) are non-isomorphic, but, conjecturally, have isomorphic group algebra. I will talk about partial results related to this conjecture, and other connections between the representation theories of groups of the form G(O), where G is a fixed simple algebraic group, and O ranges over the collection of rings of integers of all local fields.