Modular differential equations of W(Dn)-invariant Jacobi forms

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Modular differential equations of W(Dn)-invariant Jacobi forms. / Adler, D.; Gritsenko, V.

In: Journal of Geometry and Physics, Vol. 206, 01.12.2024.

Research output: Contribution to journal › Article › peer-review

Author

Adler, D. ; Gritsenko, V. / Modular differential equations of W(Dn)-invariant Jacobi forms. In: Journal of Geometry and Physics. 2024 ; Vol. 206.

BibTeX

@article{fbb7f89de1d84d74813ebc3b47d2ff8d,

title = "Modular differential equations of W(Dn)-invariant Jacobi forms",

abstract = "We study rings of weak Jacobi forms invariant with respect to the action of the Weyl group for the root systems Cn and Dn, and provide an explicit construction of generators of such rings by using modular differential operators. The construction of generators in the form of a Dn-tower (n≥2) gives a simple proof that these graded rings of Jacobi forms are polynomial. We study in detail modular differential equations (MDEs), which are satisfied by generators of index 1. Interesting anomalies are noticed for the lattices D4, D8 and D12. In particular, some generators for these lattices satisfy the Kaneko–Zagier type MDEs of order 2 or MDEs of order 1 similar to the differential equation of the elliptic genus of three-dimensional Calabi–Yau manifolds. {\textcopyright} 2024",

keywords = "Elliptic genera, Invariant theory, Jacobi forms, Modular differential equations",

author = "D. Adler and V. Gritsenko",

note = "Export Date: 19 October 2024 CODEN: JGPHE Адрес для корреспонденции: Adler, D.; Saint Petersburg University, 7/9 Universitetskaya nab., Russian Federation; эл. почта: dmitry.v.adler@gmail.com",

year = "2024",

month = dec,

day = "1",

doi = "10.1016/j.geomphys.2024.105339",

language = "Английский",

volume = "206",

journal = "Journal of Geometry and Physics",

issn = "0393-0440",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Modular differential equations of W(Dn)-invariant Jacobi forms

AU - Adler, D.

AU - Gritsenko, V.

N1 - Export Date: 19 October 2024 CODEN: JGPHE Адрес для корреспонденции: Adler, D.; Saint Petersburg University, 7/9 Universitetskaya nab., Russian Federation; эл. почта: dmitry.v.adler@gmail.com

PY - 2024/12/1

Y1 - 2024/12/1

N2 - We study rings of weak Jacobi forms invariant with respect to the action of the Weyl group for the root systems Cn and Dn, and provide an explicit construction of generators of such rings by using modular differential operators. The construction of generators in the form of a Dn-tower (n≥2) gives a simple proof that these graded rings of Jacobi forms are polynomial. We study in detail modular differential equations (MDEs), which are satisfied by generators of index 1. Interesting anomalies are noticed for the lattices D4, D8 and D12. In particular, some generators for these lattices satisfy the Kaneko–Zagier type MDEs of order 2 or MDEs of order 1 similar to the differential equation of the elliptic genus of three-dimensional Calabi–Yau manifolds. © 2024

AB - We study rings of weak Jacobi forms invariant with respect to the action of the Weyl group for the root systems Cn and Dn, and provide an explicit construction of generators of such rings by using modular differential operators. The construction of generators in the form of a Dn-tower (n≥2) gives a simple proof that these graded rings of Jacobi forms are polynomial. We study in detail modular differential equations (MDEs), which are satisfied by generators of index 1. Interesting anomalies are noticed for the lattices D4, D8 and D12. In particular, some generators for these lattices satisfy the Kaneko–Zagier type MDEs of order 2 or MDEs of order 1 similar to the differential equation of the elliptic genus of three-dimensional Calabi–Yau manifolds. © 2024

KW - Elliptic genera

KW - Invariant theory

KW - Jacobi forms

KW - Modular differential equations

U2 - 10.1016/j.geomphys.2024.105339

DO - 10.1016/j.geomphys.2024.105339

M3 - статья

VL - 206

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

ER -

ID: 126165378