Proofs of Ibukiyama's conjectures on Siegel modular forms of half-integral weight and of degree 2

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 SO5 and Gan-Ichino's multiplicity formula on the metaplectic group Mp(4). In the proof, the representation theory of the Jacobi groups also plays an important role.

Automated summary

The study uses complex mathematical concepts and multiplicity formulas to prove Ibukiyama's conjectures on Siegel modular forms of half-integral weight and of degree 2, highlighting the significant role of representation theory of the Jacobi groups in the proof.