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Weil Representations of Symplectic Groups Over Rings
Author(s) -
Cliff Gerald,
McNeilly David,
Szechtman Fernando
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610700001381
Subject(s) - mathematics , symplectic geometry , ideal (ethics) , prime (order theory) , integer (computer science) , ring (chemistry) , representation (politics) , combinatorics , field (mathematics) , ring of integers , pure mathematics , discrete mathematics , algebra over a field , algebraic number field , computer science , chemistry , philosophy , organic chemistry , epistemology , politics , political science , law , programming language
We are interested in Weil representations of Sp(2 n , R ), where R is the ring Z / p l Z , p is an odd prime and l is a positive integer, or, more generally, R = O/p l , 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(2 n , O) has to factor through a representation of Sp(2 n , O/p l ) for some l .