Siegel modular forms and finite symplectic groups
نویسندگان
چکیده
منابع مشابه
Siegel Modular Forms and Finite Symplectic Groups
The finite symplectic group Sp(2g) over the field of two elements has a natural representation on the vector space of Siegel modular forms of given weight for the principal congruence subgroup of level two. In this paper we decompose this representation, for various (small) values of the genus and the level, into irreducible representations. As a consequence we obtain uniqueness results for cer...
متن کاملSymplectic Transvectant and Siegel Modular Forms
We introduce a differential operator invariant under the symplectic group Sp(2n, C). A connection with a Rankin Cohen bracket for Siegel modular forms of genus n is sketched.
متن کاملSiegel Modular Forms
These are the lecture notes of the lectures on Siegel modular forms at the Nordfjordeid Summer School on Modular Forms and their Applications. We give a survey of Siegel modular forms and explain the joint work with Carel Faber on vector-valued Siegel modular forms of genus 2 and present evidence for a conjecture of Harder on congruences between Siegel modular forms of genus 1 and 2.
متن کاملCodes and Siegel modular forms
It is proved that the ring of Siegel modular forms in any genus is determined by doubly-even self-dual codes and the theta relations. The (higher) weight polynomials of such codes are proved to be the generators of the ring of invariants of a polynomial ring in 2 g variables under a certain speciied nite group. Moreover codes are uniquely determined by their weight polynomials.
متن کاملSiegel Modular Forms and Representations
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Theoretical and Mathematical Physics
سال: 2009
ISSN: 1095-0761,1095-0753
DOI: 10.4310/atmp.2009.v13.n6.a4