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- W2950262502 abstract "We study Hecke operators on vector-valued modular forms for the Weil representation $rho_L$ of a lattice $L$. We first construct Hecke operators $mathcal{T}_r$ that map vector-valued modular forms of type $rho_L$ into vector-valued modular forms of type $rho_{L(r)}$, where $L(r)$ is the lattice $L$ with rescaled bilinear form $(cdot, cdot)_r = r (cdot, cdot)$, by lifting standard Hecke operators for scalar-valued modular forms using Siegel theta functions. The components of the vector-valued Hecke operators $mathcal{T}_r$ have appeared in [Comm. Math. Phys. 350 (2017), 1069-1121] as generating functions for D4-D2-D0 bound states on K3-fibered Calabi-Yau threefolds. We study algebraic relations satisfied by the Hecke operators $mathcal{T}_r$. In the particular case when $r=n^2$ for some positive integer $n$, we compose $mathcal{T}_{n^2}$ with a projection operator to construct new Hecke operators $mathcal{H}_{n^2}$ that map vector-valued modular forms of type $rho_L$ into vector-valued modular forms of the same type. We study algebraic relations satisfied by the operators $mathcal{H}_{n^2}$, and compare our operators with the alternative construction of Bruinier-Stein [Math. Z. 264 (2010), 249-270] and Stein [Funct. Approx. Comment. Math. 52 (2015), 229-252]." @default.
- W2950262502 created "2019-06-27" @default.
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- W2950262502 date "2019-05-25" @default.
- W2950262502 modified "2023-09-29" @default.
- W2950262502 title "Hecke Operators on Vector-Valued Modular Forms" @default.
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- W2950262502 doi "https://doi.org/10.3842/sigma.2019.041" @default.
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