  Let K be a local non-archimedian field, F=K((t)) and let G be a split
semi-simple group. The purpose of this paper is to study certain analogs of
spherical (and Iwahori) Hecke algebras for representations of the group G(F)
and its central extension by means of K*. For instance our spherical Hecke
algebra corresponds to the subgroup G(A) where A is the subring $\calO_K((t))$
where $\calO_K\subset K$ is the ring of integers. It turns out that for generic
level the spherical Hecke algebra is trivial; however, on the critical level it
is quite large. On the other hand we expect that the size of the corresponding
Iwahori-Hecke algebra does not depend on a choice of a level (details will be
considered in another publication).
