Indecomposable Harish-Chandra Modules for Jacobi Groups

Conference paper
Part of the Contributions in Mathematical and Computational Sciences book series (CMCS, volume 10)


We describe some indecomposable \(({\mathfrak {g}},{\mathrm {K}})\)-modules for Jacobi groups that admit an automorphic realization with possible singularities. A particular tensor product decomposition of universal enveloping algebras of Jacobi Lie algebras, which does not lift to the groups, allows us to study distinguished highest weight modules for the Heisenberg group. We encounter modified theta series as components of vector-valued Jacobi forms, whose arithmetic type is not completely reducible.


Jacobi Group Harish-Chandra Modules Jacobi Forms Highest Weight Modules Theta Series 
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The author thanks the referee for comments greatly improving readability of this paper. The author was partially supported by Vetenskapsrøadet Grant 2015-04139.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institutionen för Matematiska vetenskaperChalmers tekniska högskola och Göteborgs UniversitetGöteborgSweden

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