By David Ginzburg, Stephen Rallis, David Soudry

ISBN-10: 9814304980

ISBN-13: 9789814304986

Lawsuits of the Intl convention held to honor the sixtieth birthday of A.M. Naveira. convention was once held July 8-14, 2002 in Valencia, Spain. For graduate scholars and researchers in differential geometry 1. creation -- 2. On sure residual representations -- three. Coefficients of Gelfand-Graev kind, of Fourier-Jacobi variety, and descent -- four. a few double coset decompositions -- five. Jacquet modules of parabolic inductions: Gelfand-Graev characters -- 6. Jacquet modules of parabolic inductions: Fourier-Jacobi characters -- 7. The tower estate --8. Non-vanishing of the descent I -- nine. Non-vanishing of the descent II -- 10. international genericity of the descent and international integrals -- eleven. Langlands (weak) functorial elevate and descent

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**Example text**

Let ϕσ be a cusp form in the space of σ. Define ϕσ (g)E ψℓ,w0 (g, fτ¯,¯s )dg. 19) GF \GA This the L2 -pairing between the complex conjugate of σ and σψℓ,w0 (Rτ¯,¯s ). 18). ,τℓ , the extension E/F are all unramified, and ψ is normalized (outside S). 14). It will be convenient to re-denote F Jψφℓ ,γ (E(·, fτ¯,¯s ))(h) = F Jψφℓ ,γ (E(h, fτ¯,¯s )). 21) ˆ ℓ (A). 16), F Jψφℓ ,γ (E(h, fτ¯,¯s ) is an automorphic function on GA = H point, we should remember that, in case H is metaplectic, ψ enters in the data of fτ¯,¯s , and hence in the data of the Eisenstein series; denote it now by E(h, fτ¯,¯s,ψ ).

2. 6). (m−ℓ−1) We will sometimes write ωψ,γ = ωψ,γ . If h(V ) is symplectic, we let γ = 1 and ωψ,1 = ωψ (on HWm,ℓ+1 (A) ⋊ Sp(Wm,ℓ+1 )A ). 12) and in case h(V ) is symplectic, denote ˆℓ = H Sp(Wm,ℓ+1 ), if H = Sp(V ) Sp(Wm,ℓ+1 ), if H = Sp(V ). 13) Finally, in case ℓ = m − 1, Wm,ℓ+1 = {0}, we replace HWm,ℓ+1 by the simple root subgroup in the Siegel radical, and we replace ωψ,γ by ψE,−1 . 5in master Coefficients of Gelfand-Graev Type, of Fourier-Jacobi Type, and Descent 45 ˆ m−1 = {1}. Note, that the definitions above are meaningful for ℓ = 0.

The extension E/F are all unramified, and ψ is normalized (outside S). 14). It will be convenient to re-denote F Jψφℓ ,γ (E(·, fτ¯,¯s ))(h) = F Jψφℓ ,γ (E(h, fτ¯,¯s )). 21) ˆ ℓ (A). 16), F Jψφℓ ,γ (E(h, fτ¯,¯s ) is an automorphic function on GA = H point, we should remember that, in case H is metaplectic, ψ enters in the data of fτ¯,¯s , and hence in the data of the Eisenstein series; denote it now by E(h, fτ¯,¯s,ψ ). 13), F Jψφℓ ,γ (E(h, fτ¯,¯s,ψα )) = F Jψφℓ ,γ (E(h, fτ¯⊗χα ,¯s,ψ )). 22) Let ϕσ be a cusp form in the space of σ.

### The Descent Map from Automorphic Representations of Gl (n) to Classical Groups by David Ginzburg, Stephen Rallis, David Soudry

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