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Journal of the London Mathematical Society 2000 62(2):423-436; doi:10.1112/S0024610700001381
© 2000 by London Mathematical Society
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© The London Mathematical Society

Weil Representations of Symplectic Groups Over Rings

Gerald Cliff, David McNeilly and Fernando Szechtman

Department of Mathematical Sciences, University of Alberta Edmonton, Alberta, Canada T6G 2G1
Instituto de Matematica y Estadistica, Universidad de la Republica Montevideo, Uruguay

Received 3 September 1999.

We are interested in Weil representations of Sp(2n, R), where R is the ring Z/plZ, p is an odd prime and l is a positive integer, or, more generally, R = O/pl, where O is the ring of integers of a local field, p is the maximal ideal of O and O/p has odd characteristic. One reason for this interest is that a continuous finite-dimensional complex representation of Sp(2n, O) has to factor through a representation of Sp(2n, O/pl) for some l.


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