Person:

Schmid, Wilfried

We present an application of Hodge theory towards the study of irreducible unitary representations of reductive Lie groups. We describe a conjecture about such representations and discuss some progress towards its proof.

Many important analytic statements about automorphic forms, such as the analytic continuation of certain L-functions, rely on the well-known rapid decay of K-finite cusp forms on Siegel sets. We extend this here to prove a more general decay statement along sets much larger than Siegel sets. We also state and prove the decay for smooth but not necessarily K-finite cusp forms. We shall use this to establish new results about the analytic continuation of L-functions. Our decay statements also close a gap in the literature on L-functions.