Related papers: Parabolic Simple $\mathscr{L}$-Invariants

We study a problem concerning parabolic induction in certain $p$-adic unitary groups. More precisely, for $E/F$ a quadratic extension of $p$-adic fields the associated unitary group $G=\mathrm{U}(n,n+1)$ contains a parabolic subgroup $P$…

Motivated by the study of trilinear forms for complex representations, we investigate the space of $G$-invariant linear forms on tensor products of irreducible admissible representations of $G = \mathrm{GL}_2(\mathbb{Q}_p)$ over…

Consider the moment map $\mu \colon T^*(\mathfrak{p} \times \mathbb{C}^n) \to \mathfrak{p}^*$ for a parabolic subalgebra $\mathfrak{p}$ of $\mathfrak{gl}_n(\mathbb{C})$. We prove that the preimage of $0$ under $\mu$ is a complete…

Let $F/F_0$ be a quadratic extension of non-Archimedean locally compact fields of residual characteristic $p\neq2$, and let $\sigma$ denote its non-trivial automorphism. Let $R$ be an algebraically closed field of characteristic different…

Let $\Pi$ be a regular algebraic cuspidal automorphic representation (RACAR) of $\mathrm{GL}_3(\mathbb{A}_{\mathbb{Q}})$. When $\Pi$ is $p$-nearly-ordinary for the maximal standard parabolic with Levi $\mathrm{GL}_1 \times \mathrm{GL}_2$,…

The global Langlands conjecture for $\text{GL}_n$ over a number field $F$ predicts a correspondence between certain algebraic automorphic representations $\pi$ of $\text{GL}_n(\mathbb{A}_F)$ and certain families $\{ \rho_{\pi,\ell} \}_\ell$…

We strengthen the local-global compatibility of Langlands correspondences for $GL_{n}$ in the case when $n$ is even and $l\not=p$. Let $L$ be a CM field and $\Pi$ be a cuspidal automorphic representation of $GL_{n}(\mathbb{A}_{L})$ which is…

We study the following question: given a locally compact group when does its Fourier algebra coincide with the subalgebra of the Fourier-Stieltjes algebra consisting of functions vanishing at infinity? We provide sufficient conditions for…

Let $\Pi$ be an irreducible unitary completion of a locally algebraic ${\rm GL}_2(\qp)$-representation. We describe those first-order deformations of $\Pi$ which are themselves completions of a locally algebraic representation. This answers…

By the theory of Colmez and Fontaine, a de Rham representation of the Galois group of a local field roughly corresponds to a representation of the Weil-Deligne group equipped with an admissible filtration on the underlying vector space.…

If a $p$-adic Galois representation $\rho_{f,\nu}:\Gamma_{\mathbb Q} \to \GL_2(E_{f,\nu})$ attached to some eigenform $f$ is residually reducible it will have 2 non-isomorphic reductions, which have the same semi-simplification. In this…

Let $p$ be a prime number, $F $ a non-archimedean local field with residue characteristic $p$, and $R$ an algebraically closed field of characteristic different from $ p$. We thoroughly investigate the irreducible smooth $R$-representations…

Let $K$ be a finite extension of $\mathbb{Q}_p$, and $\rho$ be an $n$-dimensional (non-critical generic) crystabelline representation of the absolute Galois group of $K$ of regular Hodge-Tate weights. We associate to $\rho$ an explicit…

Let pi be a regular algebraic cuspidal automorphic representation of GL(2) over an imaginary quadratic number field K such that the central character of pi is invariant under the non-trivial automorphism of K. We show that pi is associated…

We construct an explicit sequence $V_{k_n,a_n}$ of crystalline representations of exceptional weights converging to a given irreducible two-dimensional semi-stable representation $V_{k,{\mathcal{L}}}$ of…

We generalize Breuil-Hellmann-Schraen's local model for the trianguline variety to certain points with non-regular Hodge-Tate weights. With the local models we are able to prove, under the Taylor-Wiles hypothesis, the existence of certain…

We prove that the continuous group cohomology groups of a locally profinite group $ G $ with coefficients in a smooth $ k $-representation $ \pi $ of $ G $ are isomorphic to the $ \mathrm{Ext}$-groups $ \mathrm{Ext}^i_G(\mathbb{1},\pi) $…

Suppose that F/F+ is a CM extension of number fields in which the prime p splits completely and every other prime is unramified. Fix a place w|p of F. Suppose that rbar : Gal(F-bar/F) -> GL_3(Fp-bar) is a continuous irreducible Galois…

In this paper we study the images of certain families $\{\rho_{\pi,\ell} \}_\ell$ of $G_2$-valued Galois representations of $\mbox{Gal}(\overline{F}/F)$ associated to $L$-algebraic regular, self-dual, cuspidal automorphic representations…

The goal of this paper is to remove the irreducibility hypothesis in a theorem of Richard Taylor describing the image of complex conjugations by $p$-adic Galois representations associated with regular, algebraic, essentially self-dual,…