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The formal degree conjecture relates the formal degree of an irreduciblesquare-integrable representation of a reductive group over a local field to thespecial value of the adjoint $\gamma$-factor of its $L$-parameter. In thispaper, we prove the formal degree conjecture for odd special orthogonal andmetaplectic groups in the generic case, which combined with Arthur's work onthe local Langlands correspondence implies the conjecture in full generality.

On the formal degrees of square-integrable representations of odd special orthogonal and metaplectic groups