On vector-valued Poincaré series of weight 2

Abstract

Given a pair $(\Gamma ,\rho )$ of a Fuchsian group of the first kind, and a unitary representation $\rho$ of $\Gamma$ of arbitrary rank, the problem of construction of vector-valued Poincaré series of weight 2 is considered. Implications in the theory of parabolic bundles are discussed. When the genus of the group is zero, it is shown how an explicit basis for the space of these functions can be constructed.

Final version, 21 pages. To appear in the Journal of Geometry and Physics (2017)

References in corpus (1)

• Vector-valued automorphic forms and vector bundles

Cited by in corpus (2)

• Poincaré square series of small weight
• Logarithmic connections, WZNW action, and moduli of parabolic bundles on the sphere