No abstract uploaded!

No abstract uploaded!

Let$U$be an open subset of a complex locally convex space$E$, and$H(U)$the space of holomorphic functions from$U$to$C$. If the dual$E′$of$E$is nuclear with respect to the topology generated by the absolutely convex compact subsets of$E$, then it is shown that$H(U)$endowed with the compact open topology is a nuclear space. In particular, if$E$is the strong dual of a Fréchet nuclear space, then$H(U)$is a Fréchet nuclear space.

We introduce the$generic central character$of an irreducible discrete series representation of an affine Hecke algebra. Using this invariant we give a new classification of the irreducible discrete series characters for all abstract affine Hecke algebras (except for the types ${E_{n}^{(1)}}$ , n=6, 7, 8) with$arbitrary positive parameters$and we prove an explicit product formula for their formal degrees (in all cases).

No abstract uploaded!