Weil representations and theta functionals on surfaces (Q2875948)

The aim of the paper is to generalize the theory of Weil representations and theta functionals for curves to surfaces over a finite field and for arithmetic surfaces. First the author constructs the Weil representation for \(\mathrm{SL}_2\) over a two-dimensional local field. Then theta functionals are considered in the function field case and subsequently in the arithmetic surface case. The limit theta functional is in special cases the theta functional studied earlier by the author [Duke Math. J. 143, No. 1, 17--39 (2008; Zbl 1216.11051)] and it is invariant under loop groups \(\mathrm{SL}_2\).NEWLINENEWLINEFor the entire collection see [Zbl 1285.00037].