Some vector-valued singular automorphic forms on U(2, 2) and their restriction to Sp(1, 1)

Atsuo Yamauchi, Hiroaki Narita

Research output: Contribution to journalArticle

Abstract

In this paper we provide a construction of theta series on the real symplectic group of signature (1,1) or the 4-dimensional hyperbolic space. We obtain these by considering the restriction of some vector-valued singular theta series on the unitary group of signature (2,2) to this indefinite symplectic group. Our (vector-valued) theta series are proved to have algebraic Fourier coefficients, and lead to a new explicit construction of automorphic forms generating quaternionic discrete series representations and automorphic functions on the hyperbolic space.

Original languageEnglish
Article number1250104
JournalInternational Journal of Mathematics
Volume23
Issue number10
DOIs
Publication statusPublished - 2012 Oct 1
Externally publishedYes

Fingerprint

Theta Series
Automorphic Forms
Symplectic Group
Hyperbolic Space
Restriction
Signature
Automorphic function
Series Representation
Unitary group
Fourier coefficients

Keywords

  • 4-dimensional hyperbolic space
  • quaternionic discrete series representation
  • real symplectic group of signature (1+,1-)
  • theta series
  • unitary group of signature (2+,2-)

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Some vector-valued singular automorphic forms on U(2, 2) and their restriction to Sp(1, 1). / Yamauchi, Atsuo; Narita, Hiroaki.

In: International Journal of Mathematics, Vol. 23, No. 10, 1250104, 01.10.2012.

Research output: Contribution to journalArticle

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