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Real Group Orbits on Flag Manifolds Read chapter Read first chapter

2013 | OriginalPaper | Chapter

Weak Harmonic Maaß Forms and the Principal Series for \(SL(2, \mathbb{R})\)

Authors : Peter Kostelec, Stephanie Treneer, Dorothy Wallace

Published in: Lie Groups: Structure, Actions, and Representations

Publisher: Springer New York

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Abstract

We use the representation theory of \(SL(2, \mathbb{R})\) to construct examples of functions with transformation properties associated to classical modular forms and Maaß wave forms. We show that for special eigenvalues of the Laplacian, a Maaß wave form may be associated naturally with both a weak harmonic Maaß form and a classical modular form, leading to examples of weak harmonic Maaß forms for all even negative integer weights.

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previous chapter Center , Cascade of Orthogonal Roots, and a Construction of Lipsman–Wolf
next chapter Holomorphic Realization of Unitary Representations of Banach–Lie Groups
Literature
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K. Bringman and K. Ono, Dyson’s Ranks and Maaß Forms, Ann. Math. 171 1 (2010), 419–449.
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[7]
P. Kostelec, Nonholomorphic Cusp Forms, Ph.D thesis, Dartmouth College, 1992.
[8]
S. Lang, \(SL_{2}(\mathbb{R})\), Graduate Texts in Mathematics, Vol. 105, Springer-Verlag, NY, 1985.
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Metadata
Title
Weak Harmonic Maaß Forms and the Principal Series for
Authors
Peter Kostelec
Stephanie Treneer
Dorothy Wallace
Copyright Year
2013
Publisher
Springer New York
Book
Lie Groups: Structure, Actions, and Representations

Print ISBN: 978-1-4614-7192-9

Electronic ISBN: 978-1-4614-7193-6

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-1-4614-7193-6_9

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