On vector valued automorphic forms for the Weil representation

Oliver Stein

On vector valued automorphic forms for the Weil representation

Number Theory 2024-11-06 v3

Authors: Oliver Stein

Abstract

We develop a theory of vector valued automorphic forms associated to the Weil representation $\omega_f$ and corresponding to vector valued modular forms transforming with the ``finite'' Weil representation $\rho_L$ . For each prime $p$ we determine the structure of a vector valued spherical Hecke algebra depending on $\omega_f$ , which acts on the space of automorphic forms.

Keywords

weyl group representations hecke algebra modular forms

Cite

@article{arxiv.2108.06544,
  title  = {On vector valued automorphic forms for the Weil representation},
  author = {Oliver Stein},
  journal= {arXiv preprint arXiv:2108.06544},
  year   = {2024}
}

Comments

This is replacement for the originally submitted paper due to several (minor) mistakes. After thorough revision this version is split into two papers, of which the first part replaces the original paper. The second part is submitted separately

On vector valued automorphic forms for the Weil representation

Abstract

Keywords

Cite

Comments

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