We address the problem of the determination of the images of the Galois representations attached to genus 2 Siegel cusp forms of level 1 having multiplicity one. These representations are symplectic. We prove that the images are as large as possible for almost every prime, if the Siegel cusp form is not a Maass spezialform and verifies two easy to check conditions.
Uniform behavior of families of Galois representations on Siegel modular forms and the Endoscopy Conjecture
Theta operators on Siegel modular forms and Galois representations
Torsion in the cohomology of congruence subgroups of SL(4,Z) and Galois representations
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