Eichler-Shimura isomorphism for complex hyperbolic lattices

Abstract

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

14 pages

Cited by in corpus (3)

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