Borcherds Products Everywhere

Gritsenko, Valery; Poor, Cris; Yuen, David S.

doi:10.1016/j.jnt.2014.07.028

Cited by 23 publications

(52 citation statements)

References 32 publications

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“…In this subsection, we define six reflective modular forms using a modular form of singular weight for the lattice

2 U \oplus 3 A_{2}

proposed in [, Section 4]. This modular form also gives interesting series of canonical differential forms on Siegel modular three‐folds constructed with theta‐blocks (see ). Lemma The function

σ_{A_{2}} false(τ, frakturz false) = σ_{A_{2}} false(τ, z_{1}, z_{2} false) = \frac{ϑ false(τ, z_{1} false) ϑ false(τ, z_{2} false) ϑ false(τ, z_{1} + z_{2} false)}{η (τ)} \in J_{1, A_{2}} false(v_{η}^{8} false)

is a holomorphic Jacobi form of singular weight which is anti‐invariant with respect to the 6‐reflections from

normalO (A_{2})

.…”

Section: Reflective Towers Of Jacobi Liftingsmentioning

confidence: 99%

“…In this subsection, we define six reflective modular forms using a modular form of singular weight for the lattice 2U ⊕ 3A 2 proposed in [18,Section 4]. This modular form also gives interesting series of canonical differential forms on Siegel modular three-folds constructed with theta-blocks (see [31]).…”

Section: The Jacobi Lifting and Fourier Coefficients Of Modular Formsmentioning

confidence: 99%

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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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“…In this subsection, we define six reflective modular forms using a modular form of singular weight for the lattice

2 U \oplus 3 A_{2}

proposed in [, Section 4]. This modular form also gives interesting series of canonical differential forms on Siegel modular three‐folds constructed with theta‐blocks (see ). Lemma The function

σ_{A_{2}} false(τ, frakturz false) = σ_{A_{2}} false(τ, z_{1}, z_{2} false) = \frac{ϑ false(τ, z_{1} false) ϑ false(τ, z_{2} false) ϑ false(τ, z_{1} + z_{2} false)}{η (τ)} \in J_{1, A_{2}} false(v_{η}^{8} false)

is a holomorphic Jacobi form of singular weight which is anti‐invariant with respect to the 6‐reflections from

normalO (A_{2})

.…”

Section: Reflective Towers Of Jacobi Liftingsmentioning

confidence: 99%

Section: The Jacobi Lifting and Fourier Coefficients Of Modular Formsmentioning

confidence: 99%

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

Gritsenko

Nikulin

2017

Proc. London Math. Soc.

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“…A nice description of the relevant aspects of this form can be found in the work of Gritsenko [11], from which we borrow heavily.…”

Section: The Borcherds Modular Form φ 12mentioning

confidence: 99%

“…In the interpretation of Φ12 as a denominator for the fake Monster Lie algebra, one views (A, B, C) as a Weyl vector; see [10,11] for details and section 4 for further comments on potential applications of the algebraic structure to physics.…”

Section: Jhep10(2017)121mentioning

confidence: 99%

Heterotic sigma models on T 8 and the Borcherds automorphic form Φ12

Harrison

Kachru

Paquette

et al. 2017

J. High Energ. Phys.

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Abstract:We consider the spectrum of BPS states of the heterotic sigma model with (0, 8) supersymmetry and T 8 target, as well as its second-quantized counterpart. We show that the counting function for such states is intimately related to Borcherds' automorphic form Φ 12 , a modular form which exhibits automorphy for O(2, 26; Z). We comment on possible implications for Umbral moonshine and theories of AdS 3 gravity.

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“…The second method is the multiplicative lifting (Borcherds automorphic product, see [1], [2]) in a form, proposed by Gritsenko-Nikulin in [12], which sends a weakly holomorphic Jacobi form of weight 0 to a meromorphic paramodular form. In [14], V. Gritsenko, C. Poor and D. Yuen investigated the paramodular forms which are simultaneously Borcherds products and Gritsenko lifts.…”

Section: Introductionmentioning

confidence: 99%