Generalized transvectants and Siegel modular forms
نویسندگان
چکیده
منابع مشابه
Generalized Transvectants and Siegel Modular Forms
We introduce a differential operator invariant under the special linear group SL(2n, C), and, as a consequence, the symplectic group Sp(2n, C). Connections with generalized Rankin–Cohen brackets for Siegel modular forms of genus n are sketched.
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We discuss the amazing interconnections between normal form theory, classical invariant theory and transvectants, modular forms and Rankin–Cohen brackets, representations of the Heisenberg algebra, differential invariants, solitons, Hirota operators, star products and Moyal brackets and coherent states. † Supported in part by NSF Grant DMS 98–03154.
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This paper explicitly describes the procedure of associating an automorphic representation of PGSp(2n, A) with a Siegel modular form of degree n for the full modular group Γn = Sp(2n, Z), generalizing the well-known procedure for n = 1. This will show that the so-called “standard” and “spin” L-functions associated with such forms are obtained as Langlands L-functions. The theory of Euler produc...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2007
ISSN: 0196-8858
DOI: 10.1016/j.aam.2005.11.001