The Jacobi group and its holomorphic discrete series representations on Siegel-Jacobi domains

This is the summary of a part of the talk delivered at the workshop held at the Tambov University in September 2012, reporting several results on Jacobi groups and its holomorphic representations published by the authors.

Jacobi group, Siegel-Jacobi domain, canonical automorphy factor, canonical kernel function, scalar holomorphic discrete series

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3. S. Berceanu, “A holomorphic representation of Jacobi algebra in several dimensions”, The Theta Foundation, Perspectives in Operator Algebras and Mathematical Physics (Bucharest, August 10-17, 2005), Theta Series in Advanced Mathematics, 11, eds. F.P. Boca, R. Purice, S. Strˇatilˇa, Conference Proceedings, 2008, 1-25.

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