Proofs of Ibukiyama's conjectures on Siegel modular forms of half-integral weight and of degree 2
Abstract
We prove Ibukiyama's conjectures on Siegel modular forms of half-integral weight and of degree 2 by using Arthur's multiplicity formula on the split odd special orthogonal group 5 and Gan-Ichino's multiplicity formula on the metaplectic group 4. In the proof, the representation theory of the Jacobi groups also plays an important role.
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