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Hecke operators on vector-valued modular forms Joshi, Aniket


We study Hecke operators on vector-valued modular forms (vvmfs) for the Weil representation of a lattice $L$. In particular, we construct Hecke operators that map vector-valued modular forms (vvmfs) of a lattice $L$ to those of the same lattice $L$, and also Hecke operators that map vvmfs to those of a rescaled lattice. The components of these Hecke operators 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 and compare our operators with the alternative construction of Bruinier-Stein. This is joint work done with V. Bouchard and T. Creutzig.

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