For G=GSp_4 we construct an automorphic sheaf correspinding to a G^L-local system on a curve X such that its standard representation is an irreducible local system of rank 4 on X. This is obtained an an application of some more general results related to the geometric theta-lifting.
Two Propositions Involving the Standard Representation of $S_n$
Ext-Multiplicity Theorem for Standard Representations of $(\mathrm{GL}_{n+1},\mathrm{GL}_n)$
Irreducible Local Systems on Nilpotent Orbits
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