TY - JOUR
T1 - Some vector-valued singular automorphic forms on U(2, 2) and their restriction to Sp(1, 1)
AU - Yamauchi, Atsuo
AU - Narita, Hiro Aki
N1 - Funding Information:
The second author was partially supported by Grant-in-Aid for Young Scientists (B) 18749008, JSPS.
PY - 2012/10
Y1 - 2012/10
N2 - 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.
AB - 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.
KW - 4-dimensional hyperbolic space
KW - quaternionic discrete series representation
KW - real symplectic group of signature (1+,1-)
KW - theta series
KW - unitary group of signature (2+,2-)
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U2 - 10.1142/S0129167X12501042
DO - 10.1142/S0129167X12501042
M3 - Article
AN - SCOPUS:84869379918
SN - 0129-167X
VL - 23
JO - International Journal of Mathematics
JF - International Journal of Mathematics
IS - 10
M1 - 1250104
ER -