Title: Local root numbers for Heisenberg representations 


Abstract: On the Langlands program, explicit computation of the local root numbers 
(or epsilon factors) for Galois representations is an integral part.
But for arbitrary Galois representation of higher dimension, we do not
have explicit formula for local root numbers. In our recent work
(joint with Ernst-Wilhelm Zink) we consider Heisenberg representation
(i.e., it represents commutators by scalar matrices) of the Weil
group W_F of a p-adic number field F and we give invariant formulas for
the local root numbers of such representations when dimensions are
 prime to p.

In my talk, first, we will discuss the arithmetic description of
Heisenberg representations and properties of root number. Then we will
explain some
 explicit results regarding local roots number of Heisenberg
representations.