Igor Ciganović (U Zagreb)

Abstract: Since irreducible unramified representations of the metaplectic group are important for the theory of automorphic forms and theta correspondance, their detailed classfication, analogous to the  case of linear groups, is provided. More precisely, it is shown that  every irreducible unramified representation of the metaplectic group  over a p-adic field, where p is not 2, is fully parabolically induced representation from unramified characters of general linear groups and a negative unramified representation of a smaller metaplectic group.  These are described in terms of parabolic induction from unitary unramified characters of general linear groups and irreducible strongly negative unramified representation of a smaller metaplectic group,  which are classified in terms of Jordan blocks. Main tools areparabolic induction and Jacquet modules.

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