Abstract
We prove the polynomiality of the bigraded ring \(J_{*,*}^{w, W}(F_4)\) of weak Jacobi forms for the root system \(F_4\) which are invariant with respect to the corresponding Weyl group. This work is a continuation of a joint article with V. A. Gritsenko, where the structure of the algebras of weak Jacobi forms related to the root systems of \(D_n\) type for \(2\leqslant n \leqslant 8\) was studied.
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Acknowledgments
The author is grateful to O. Schwarzman for the original formulation of the problem, helpful discussions of results, and useful remarks on the paper and to V. Gritsenko for supervision and very stimulating conversations.
Funding
This work was supported by International Laboratory for Mirror Symmetry and Automorphic Forms, National Research University Higher School of Economics, under Government grant no. 14.641.31.0001.
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Translated from Funktsional'nyi Analiz i Ego Prilozheniya, 2020, Vol. 54, No. 3, pp. 8-25 https://doi.org/10.4213/faa3760 .
Translated by D. V. Adler
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Adler, D.V. The Structure of the Algebra of Weak Jacobi Forms for the Root System \(F_4\). Funct Anal Its Appl 54, 155–168 (2020). https://doi.org/10.1134/S0016266320030016
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DOI: https://doi.org/10.1134/S0016266320030016