Symmetric tensor representations, quasimodular forms, and weak Jacobi forms
Quasimodular forms, Rankin-Cohen brackets, Vector-valued modular forms, Weak Jacobi forms
Advances in Mathematics
We establish a correspondence between vector-valued modular forms with respect to a symmetric tensor representation and quasimodular forms. This is carried out by first obtaining an explicit isomorphism between the space of vector-valued modular forms with respect to a symmetric tensor representation and the space of finite sequences of modular forms of certain type. This isomorphism uses Rankin-Cohen brackets and extends a result of Kuga and Shimura, who considered the case of vector-valued modular forms of weight two. We also obtain a correspondence between such vector-valued modular forms and weak Jacobi forms.
Original Publication Date
DOI of published version
UNI ScholarWorks, Rod Library, University of Northern Iowa
Choie, Young Ju and Lee, Min Ho, "Symmetric tensor representations, quasimodular forms, and weak Jacobi forms" (2016). Faculty Publications. 1129.