Mixed automorphic vector bundles on Shimura varieties
Pacific Journal of Mathematics
Let S0(G, X), S0(G′, X′) be connected Shimura varieties associated to semisimple algebraic groups G, G′ defined over ℚ and Hermitian symmetric domains X, X′. Let p : G → G′ be a homomorphism of algebraic groups over ℚ that induces a holomorphic map ω : X → X′ mapping special points of X to special points of X′. Given equivariant vector bundles J, J′ on the compact duals X̌, X̌′ of the symmetric domains X, X′, we can construct a mixed automorphic vector bundle M(J, J′, p), on S0(G, X) whose sections can be interpreted as mixed automorphic forms. We prove that the space of sections of a certain mixed automorphic vector bundles is isomorphic to the space of holomorpic forms of the highest degree on the fiber product of a finite number of Kuga fiber varieties. We also prove that for each automorphism T of ℂ the conjugate τM(J, J′, p) of a mixed automorphic vector bundle M(J, J′, p) on a connected Shimura variety S0(G, X) can be canonically realized as a mixed automorphic vector bundle M(J1, J′1, p1) on another connected Shimura variety S0(G1, X1) associated to a semisimple algebraic group G1 and a Hermitian symmetric domain X1.
Original Publication Date
DOI of published version
Lee, Min Ho, "Mixed automorphic vector bundles on Shimura varieties" (1996). Faculty Publications. 4214.