Matching Tag: arithmetic-transfer
Arithmetic transfer conjecture for odd type ( r , 0 ) (r,0) ( r , 0 ) φ ′ ∈ C c ∞ ( G ′ ) \varphi'\in C_c^\infty(G') φ ′ ∈ C c ∞ ( G ′ ) ( c r 2 , 1 K n [ r ] × K n + 1 , 0 ) (c_r^2\\,\mathbf{1}_{K_n^{[r]}\times K_{n+1}},0) ( c r 2 , 1 K n [ r ] × K n + 1 , 0 )
Let 0 ≤ r ≤ n + 1 0\leq r\leq n+1 0 ≤ r ≤ n + 1 ε \varepsilon ε r r r W ε W_\varepsilon W ε W ε + 1 W_{\varepsilon+1} W ε + 1 n + 1 n+1 n + 1
Assume that F / F 0 F/F_0 F / F 0 n ≥ 2 n\geq2 n ≥ 2 K 0 ♭ K_0^{{{{{{{{\flat}}}}}}}} K 0 ♭ π \pi π K 0 + K_0^+ K 0 + K 0 − K_0^- K 0 −
Assume that F / F 0 F/F_0 F / F 0 K ′ ⊂ S n ( F 0 ) K'\subset S_n(F_0) K ′ ⊂ S n ( F 0 ) K 1 ⊂ U ( W 1 ) ( F 0 ) K_1\subset\mathrm{U}(W_1)(F_0) K 1 ⊂ U ( W 1 ) ( F 0 ) ω S \omega_S ω S
Lie algebra arithmetic transfer conjecture. (a) There exists ϕ ′ ∈ C c ∞ ( s ) \phi'\in C_c^\infty(\mathfrak{s}) ϕ ′ ∈ C c ∞ ( s ) ( 1 k 0 , 0 ) (\mathbf{1}_{\mathfrak{k}_0},0) ( 1 k 0 , 0 )
Let F / F 0 F/F_0 F / F 0 n ≥ 3 n\geq3 n ≥ 3 S ( F 0 ) S(F_0) S ( F 0 ) U 0 U_0 U 0 U 1 U_1 U 1 K 0 ⊂ U 0 ( F 0 ) K_0\subset U_0(F_0) K 0 ⊂ U 0 ( F 0 )
