Concrete description of the (Г, χ)-theta Fock-Bargmann space for rank one in high dimension

Abstract

We give concrete description of the -theta Fock-Bargmann space consisting of holomorphic automorphic functions associated to given discrete subgroup in of rank one and given character . It looks like a tensor product of a theta Fock-Bargmann space on the complex plane and the classical Fock-Bargmann space on . Moreover, we construct an orthonormal basis and we give explicit expression of its reproducing kernel function in terms of Riemann theta function.

Keywords:

• rank one discrete subgroup
• (Г, χ)-theta Fock-Bargmann space
• orthonormal basis
• reproducing kernel
• theta function

AMS Subject Classifications:

• 30F35
• 32A10
• 46E22
• 46E50

Acknowledgements

I am thankful to the anonymous referees for the valuable suggestions for improving the presentation of the paper.

Notes

No potential conflict of interest was reported by the author.