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The character of the Weil representation
Author(s) -
Thomas Teruji
Publication year - 2008
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/jlms/jdm098
Subject(s) - character (mathematics) , pure mathematics , mathematics , symplectic geometry , representation (politics) , subspace topology , symplectic group , pullback , function (biology) , relation (database) , space (punctuation) , vector space , field (mathematics) , algebra over a field , mathematical analysis , computer science , philosophy , geometry , linguistics , database , evolutionary biology , politics , political science , law , biology
Let V be a symplectic vector space over a finite or local field. We compute the character of the Weil representation of the metaplectic group Mp( V ). The final formulas are overtly free of choices (for example, they do not involve the usual choice of a Lagrangian subspace of V ). Along the way, in results similar to those of Maktouf, we relate the character to the Weil index of a certain quadratic form, which may be understood as a Maslov index. This relation also expresses the character as the pullback of a certain simple function from Mp( V ⊕ V ).