A classification of polyharmonic Maaß forms via quiver representations

Alfes-Neumann C, Burban I, Raum M (2022)
arXiv:2207.02278.

Preprint | Englisch
 
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Autor*in
Alfes-Neumann, ClaudiaUniBi ; Burban, Igor; Raum, Martin
Abstract / Bemerkung
We give a classification of the Harish-Chandra modules generated by the pullback to~$\SL{2}(\RR)$ of \emph{poly}harmonic Maa\ss{} forms for congruence subgroups of~$\SL{2}(\ZZ)$ with exponential growth allowed at the cusps. This extends results of Bringmann--Kudla in the harmonic case. While in the harmonic setting there are nine cases, our classification comprises ten; A new case arises in weights $k > 1$. To obtain the classification we introduce quiver representations into the topic and show that those associated with polyharmonic Maa\ss{} forms are cyclic, indecomposable representations of the two-cyclic or the Gelfand quiver. A classification of these transfers to a classification of polyharmonic weak Maa\ss{} forms. To realize all possible cases of Harish-Chandra modules we develop a theory of weight shifts for Taylor coefficients of vector-valued spectral families. We provide a comprehensive computer implementation of this theory, which allows us to provide explicit examples.
Erscheinungsjahr
2022
Zeitschriftentitel
arXiv:2207.02278
Page URI
https://pub.uni-bielefeld.de/record/2964260

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Alfes-Neumann C, Burban I, Raum M. A classification of polyharmonic Maaß forms via quiver representations. arXiv:2207.02278. 2022.
Alfes-Neumann, C., Burban, I., & Raum, M. (2022). A classification of polyharmonic Maaß forms via quiver representations. arXiv:2207.02278
Alfes-Neumann, C., Burban, I., and Raum, M. (2022). A classification of polyharmonic Maaß forms via quiver representations. arXiv:2207.02278.
Alfes-Neumann, C., Burban, I., & Raum, M., 2022. A classification of polyharmonic Maaß forms via quiver representations. arXiv:2207.02278.
C. Alfes-Neumann, I. Burban, and M. Raum, “A classification of polyharmonic Maaß forms via quiver representations”, arXiv:2207.02278, 2022.
Alfes-Neumann, C., Burban, I., Raum, M.: A classification of polyharmonic Maaß forms via quiver representations. arXiv:2207.02278. (2022).
Alfes-Neumann, Claudia, Burban, Igor, and Raum, Martin. “A classification of polyharmonic Maaß forms via quiver representations”. arXiv:2207.02278 (2022).

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