Eichler-Shimura isomorphism for complex hyperbolic lattices
Journal article, 2017

We consider the cohomology group H-1(Gamma, p) of a discrete subgroup Gamma subset of G = SU(n, 1) and the symmetric tensor representation p on S-m(c(n+1)). We give an elementary proof of the Eichler-Shimura isomorphism that harmonic forms H-1(Gamma\ G/K, p) are (0, 1)-forms for the automorphic holomorphic bundle induced by the representation S-m(C-n) of K.

Complex hyperbolic lattice

First cohomology

Eichler-Shimura isomorphism


Inkang Kim

Korea Institute for Advanced Study

Genkai Zhang

Chalmers, Mathematical Sciences, Analysis and Probability Theory

University of Gothenburg

Journal of Geometry and Physics

0393-0440 (ISSN)

Vol. 121 452-460

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