Nagoya Mathematical Journal

Some constructions of modular forms for the Weil representation of SL2(Z)

Nils R. Scheithauer

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Modular forms for the Weil representation of SL2(Z) play an important role in the theory of automorphic forms on orthogonal groups. In this paper we give some explicit constructions of these functions. As an application, we construct new examples of generalized Kac–Moody algebras whose denominator identities are holomorphic automorphic products of singular weight. They correspond naturally to the Niemeier lattices with root systems D122, E83 and to the Leech lattice.

Article information

Nagoya Math. J., Volume 220 (2015), 1-43.

Received: 9 December 2013
Revised: 20 June 2014
Accepted: 13 August 2014
First available in Project Euclid: 1 December 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F27: Theta series; Weil representation; theta correspondences
Secondary: 11F22: Relationship to Lie algebras and finite simple groups 17B65: Infinite-dimensional Lie (super)algebras [See also 22E65]

modular forms for the Weil representation automorphic products generalized Kac–Moody algebras


Scheithauer, Nils R. Some constructions of modular forms for the Weil representation of $\operatorname{SL}_{2}(\mathbb{Z})$. Nagoya Math. J. 220 (2015), 1--43. doi:10.1215/00277630-3335405.

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