... to1 2 timesress=1L(s,π,sym 2 )ε(1,π,sym 2 )L (2, π,sym 2 )G = SO(2n +1)L(1 2 ,π)ε(1 2 ,π)L(3 2 ,π)ress=1L(s,π,∧ 2 )ε(1,π,∧ 2 )L (2, π,∧ 2 )G =Spnress=1L(s,π,∧ 2 )ε(1,π,∧ 2 )L (2, π,∧ 2 )G = SO(2n).By Lemma 1, π is of G-type if and ... bymv(s)=L(2s,πv,sym 2 )ε(2s,πv,sym 2 ,ψ−1v)L(2s+1,πv,sym 2 )G = SO(2n +1),L(s,πv)ε(s,πv,ψ−1v)L(s+1,πv)L(2s,πv,∧ 2 )ε(2s,πv,∧ 2 ,ψ−1v)L(2s+1,πv,∧ 2 )G =Spn,L(2s,πv,∧ 2 )ε(2s,πv,∧ 2 ,ψ−1v)L(2s+1,πv,∧ 2 )G ... ∧ 2 )L(1+2s, π, ∧ 2 ).If G = SO(2n),m(s)=L(2s, π, ∧ 2 )ε(2s, π, ∧ 2 )L(2s +1,π,∧ 2 )=L(1 − 2s, π, ∧ 2 )L(1 + 2s, π, ∧ 2 ).9 02 EREZ LAPID AND STEPHEN RALLIS and we may use the induction hypothesis....