17 problems

Let $Q=LU$ be a parabolic subgroup of $G$, let $N_L$ be a maximal unipotent subgroup of $L$, set $N=N_LU$, and let $\xi_L$ be a generic character of $[N_L]$, extended trivially acr…

Let $\hat{\Delta}_{\mathrm{red}}=(\hat{L},\hat{H}',1,\hat{\rho}_{\hat{H}',\hat{\iota}'})$, where … Let $\pi_L$ be a tempered automorphic representation of $L(\mathbb A)$ and let…

Let $G$ be a reductive group, let $H$ be a subgroup equipped with a homomorphism $\boldsymbol{\rho}_H$ as in the BZSV setting, and let $\iota$ determine the dual homomorphism … For…

Semi-local period-integral commutator relation. Under $\thref{genassum}$,

Period-integral commutator relation. Under $\thref{commsetup}$,

Let $E$ be a field, let $G$ be a reductive group over a local field $F$, and let $Y=H\backslash G$ be a spherical variety. For a smooth admissible $G(F)$-representation $\pi$ over…

Let $\Pi_\phi=\bigcup_D\Pi_\phi(G_D)$ be the global tempered cuspidal $L$-packet and retain the notation for the models $(G_D,H_D)$, the embeddings $\nu$, and the period integrals…

Consider the first model in Table 1, $(G,H)=({\mathrm{GL}}_4\times{\mathrm{GL}}_2,{\mathrm{GL}}_2\times{\mathrm{GL}}_2)$, for which $Z_H/Z_{G,H}\cong {\mathrm{GL}}_1$. Under the no…

Let $(G,H)$ be one of the models in Table 1 other than the first, and let $D/k$ be a quaternion algebra, possibly split (or $D\in H^1(H/Z_{G,H},k)$ for Model 2). Let…

Let $\f$ and $\f'$ be factorizable vectors in representations $\c0$ and $\c0'$, respectively. Let $\a$ be the period pairing, ${\overline{\frak b}}$ the global arithmetic factor,…

Let $X=G/P$ be a homogeneous variety, let $E=L_1\oplus\cdots\oplus L_r$ be a direct sum of homogeneous line bundles, and let $Y_i$ be the zero locus of the $L_i$-component of a sec…

Let $f$ be a homogeneous polynomial defining a smooth hypersurface family, and let $\alpha_s$ be the matrices associated with the Laurent polynomial construction, with $\sigma$ the…

Let $k$ be a global field with ring of adeles ${\boldsymbol A}$, and let $D$ range over quaternion algebras over $k$. For an irreducible cuspidal automorphic representation $\pi$ o…

Let $\check{X}_t$ be the mirror family of a toric Calabi–Yau variety, let $\check{\Omega}_{\phi(q)}$ be its holomorphic volume form evaluated at the SYZ-map parameter $\phi(q)$, an…

Holonomic rank conjecture. The solution rank of $\tau$ at the point $a\in V^\vee$ is given by

Let $F$ be a number field, let $E/F$ be a quadratic extension, and let $G$ and $H$ be the unitary groups in the source. Let $\pi=\pi_n\otimes\pi_{n+1}$ be a tempered cuspidal autom…

Let $G_n\subset G_{n+1}$ be the special orthogonal groups in the Gross–Prasad setting, and let $\pi_n$ and $\pi_{n+1}$ be the associated tempered cuspidal automorphic representatio…