Related papers: Equations differentielles p-adiques et modules de …

We give another proof of Imin Chen's result that the jacobian of the modular curve X(p)_{non-split}, for p a prime number, is isogeneous to the new part of the jacobian of X_0(p^2), using only the representation theory of the group…

In this paper, the fractional differential matrices based on the Jacobi-Gauss points are derived with respect to the Caputo and Riemann-Liouville fractional derivative operators. The spectral radii of the fractional differential matrices…

We consider mod $p$ Hilbert modular forms for a totally real field $F$, viewed as sections of automorphic line bundles on Hilbert modular varieties in prime characteristic $p$. For a Hecke eigenform of arbitrary weight, we prove the…

Based on previous results of Jiang, Nien and the third author, we prove that any two minimax unitarizable supercuspidals of GL_N that have the same depth and central character admit a special pair of Whittaker functions. This result gives a…

A symmetric space analogue of Casselman's criterion for square integrability of representations of a p-adic group is established. It is described in terms of exponents of Jacquet modules along parabolic subgroups associated to the symmetric…

We continue the study of the vertex operator algebra $L(k,0)$ associated to a type $G_2^{(1)}$ affine Lie algebra at admissible one-third integer levels, $k = -2 + m + \tfrac{i}{3}\ (m\in \mathbb{Z}_{\ge 0}, i = 1,2)$, initiated in…

The local analytic classification and the description of the Galois group for complex linear analytic q-difference equations have been obtained by Ramis, Sauloy and Zhang [15, 14] under the assumption that the slopes of the Newton polygon…

Let $K$ be a finite unramified extension of $\mathbb{Q}_p$, where $p>2$. [CEGS22b] and [EG23] construct a moduli stack of two dimensional mod $p$ representations of the absolute Galois group of $K$. We show that most irreducible components…

Let p at least 5 be prime. We construct a fully faithful functor from the derived category of all smooth p-adic representations of GL_2(Q_p) (with a fixed central character) to a derived category of Ind-coherent sheaves on a stack of…

It is well known that for irreducible, square-integrable representations of a locally compact group, there exist so-called admissible vectors which allow the construction of generalized continuous wavelet transforms. In this paper we…

Let p>3 be a prime, f a positive integer and Q_{p^f} the unramified extension of Q_p of degree f. After Breuil and Paskunas, to a generic semi-simple continue modulo p representation of the absolute Galois group of Q_{p^f}, we can associate…

We construct new families of U_q(gl_n)-modules by continuation from finite dimensional representations. Each such module is associated with a combinatorial object - admissible set of relations defined in \cite{FRZ}. More precisely, we prove…

For any finite group $G$ and any prime $p$ one can ask which ordinary irreducible representations remain irreducible in characteristic $p$. We answer this question for $p=2$ when $G$ is a proper double cover of the symmetric group. Our…

We construct classes of von Neumann algebra modules by considering ``column sums" of noncommutative L^p spaces. Our abstract characterization is based on an L^{p/2}-valued inner product, thereby generalizing Hilbert C*-modules and…

Let $p>3$ be a prime number and let $G_{\mathbb{Q}_p}$ be the absolute Galois group of $\mathbb{Q}_p$. In this paper, we find Galois stable lattices in the irreducible $3$-dimensional semi-stable and non-crystalline representations of…

In this paper we study certain category of smooth modules for reductive $p$--adic groups analogous to the usual smooth complex representations but with the field of complex numbers replaced by a $\mathbb Q$--algebra. We prove some…

For the algebra L= K <x, d/dx, \int> of polynomial integro-differential operators over a field K of characteristic zero, a classification of indecomposable, generalized weight L-modules of finite length is given. Each such module is an…

We can associate an admissible unitary representation $\Pi(\rho_p)$ of $\GL_2(\Q_p)$ with every local Galois representation $\rho_p$ by the $p$-adic local Langlands correspondence. If $\rho_p$ is ordinary, we prove local and global…

This paper describes the classification of analytic $q$-difference equations. The difference Galois groups are computed. A tentative description of the universal difference Galois group is given.

Let $G$ be a $p$-adic reductive group and $R$ be a noetherian Jacobson $\mathbb{Z}[1/p]$-algebra. In this note, we show that every smooth irreducible $R$-linear representation of $G$ is admissible using the finiteness result of Dat, Helm,…