# Functors for representations of GL(n,F)

*Algebra/Geometry/Topology Seminar*

*by Peter Trapa*

*Institution:*Utah

*Date: Mon 20th April 2009*

*Time: 2:15 PM*

*Location: David Caro Building, Room 211*

*Abstract*: Let F denote a local field of characteristic zero (like the real numbers or the p-adic numbers), and let GL(n,F) denote the set of n-by-n invertible matrices over F. As the field F varies, the representation theoretic part of the local Langlands correspondence predicts relationships between the Grothendieck groups of representations of the various groups GL(n,F). Most of the talk will be an introduction to these ideas. If time permits, I will introduce some functors (defined in joint work with Dan Ciubotaru for more general groups) which implement the relationships of Grothendieck groups categorically.