A Note on Mock Automorphic Forms and the BPS Index

We discuss mock automorphic forms from the point of view of representation theory, that is, mock automorphic forms obtained from weak harmonic Maaß forms giving rise to nontrivial $(\mathfrak g,K)$-cohomology. We consider the possibility of replacing the ‘holomorphic’ condition with a “cohomological” one when generalizing to general reductive groups. Such a candidate for replacement allows for growing Fourier coefficients, in contrast to automorphic forms under the Miatello-Wallach conjecture. In the second part, we provide an overview of the connection with BPS black hole counts as a physical motivation for studying mock automorphic forms.