On the classification of automorphic products and generalized Kac–Moody algebras

Scheithauer, Nils R.

doi:10.1007/s00222-006-0500-5

Cited by 68 publications

(122 citation statements)

References 9 publications

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“…Remark Some other reflective modular forms of singular weight similar to Borcherds forms

Φ_{12}

and

Φ_{4}^{B E}

above were found by Scheithauer (see ). The reflective forms of singular weight in his class are modular with respect to congruence subgroups.…”

Section: Reflective Towers Of Jacobi Liftingssupporting

confidence: 60%

Lorentzian Kac-Moody algebras with Weyl groups of 2-reflections

Gritsenko

Nikulin

2017

Proc. London Math. Soc.

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We describe a new large class of Lorentzian Kac–Moody algebras. For all ranks, we classify 2‐reflective hyperbolic lattices S with the group of 2‐reflections of finite volume and with a lattice Weyl vector. They define the corresponding hyperbolic Kac–Moody algebras of restricted arithmetic type which are graded by S. For most of them, we construct Lorentzian Kac–Moody algebras which give their automorphic corrections: they are graded by the S, have the same simple real roots, but their denominator identities are given by automorphic forms with 2‐reflective divisors. We give exact constructions of these automorphic forms as Borcherds products and, in some cases, as additive Jacobi liftings.

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“…Remark Some other reflective modular forms of singular weight similar to Borcherds forms

Φ_{12}

and

Φ_{4}^{B E}

above were found by Scheithauer (see ). The reflective forms of singular weight in his class are modular with respect to congruence subgroups.…”

Section: Reflective Towers Of Jacobi Liftingssupporting

confidence: 60%

Lorentzian Kac-Moody algebras with Weyl groups of 2-reflections

Gritsenko

Nikulin

2017

Proc. London Math. Soc.

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“…Borcherds found some operations for constructing modular forms for the Weil representations, which were subsequently developed by Bruinier and Scheithauer, as we recall below: Pullback to a sublattice . Pushforward to an overlattice . Induction from scalar‐valued modular forms . …”

Section: Weil Representations and Borcherds Productsmentioning

confidence: 99%

“…We now turn to describing induction from scalar‐valued modular forms . Let

A

be a finite quadratic module.…”

Section: Weil Representations and Borcherds Productsmentioning

confidence: 99%

“…This is a weakly holomorphic modular form of weight

k

and type

ρ_{A}

for

{Mp}_{2} false(double-struckZ false)

. This construction is due to Borcherds [, p. 342] for

I = {0}

, and Scheithauer [, Theorem 6.2] for general

I

. We especially denote

{ind}_{A}^{{0}} = {ind}_{A}

.…”

Section: Weil Representations and Borcherds Productsmentioning

confidence: 99%

“…In some applications, the

ρ_{L}

‐valued form

f

is constructed from a scalar‐valued modular form

φ

by means of ‘induction’ (see, for example, ). In that case, the

ρ_{M}

‐valued form

g

can be expressed more explicitly in terms of

φ

(§ ).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quasi‐pullback of Borcherds products

2019

Bull. London Math. Soc.

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Lie Algebras, Vertex Algebras, and Automorphic Forms

Scheithauer¹

2010

Progress in Mathematics

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On the classification of automorphic products and generalized Kac–Moody algebras

Cited by 68 publications

References 9 publications

Lorentzian Kac-Moody algebras with Weyl groups of 2-reflections

Lorentzian Kac-Moody algebras with Weyl groups of 2-reflections

Quasi‐pullback of Borcherds products

Lie Algebras, Vertex Algebras, and Automorphic Forms

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