These notes give an account of recent work in harmonic analysis
dealing with the analytical foundations of A. Weil's theory of
metaplectic groups. It is shown that Weil's main theorem holds for
a class of functions (a certain Segal algebra) larger than that of
the Schwartz-Bruhat functions considered by Weil. The theorem is
derived here from some general results about this class which seems
to be a rather natural one in the context of Weil's theory. No
previous knowledge of the latter is assumed, however, and the
theory is developed here, step by step; Further, a complete
discussion of the Segal algebra concerned is given, with references
to the literature. Weil's metaplectic groups are somewhat easier to
investigate when the characteristic is not 2; the case of
characteristic 2 presents some special features which are fully
discussed. New problems that arise are indicated.
General
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