Related papers: Duality for generalized Gan-Gross-Prasad relevant …

Linear systems occur throughout engineering and the sciences, most notably as differential equations. In many cases the forcing function for the system is unknown, and interest lies in using noisy observations of the system to infer the…

The "quantum duality principle" states that a quantisation of a Lie bialgebra provides also a quantisation of the dual formal Poisson group and, conversely, a quantisation of a formal Poisson group yields a quantisation of the dual Lie…

In the following article, we give a description of the distingushed irreducible principal series representations of the general linear group over a p-adic field in terms of inducing datum. This provides a counter-example to a conjecture of…

We prove that the Jacquet restriction functor for a parabolic subgroup of a reductive group over a non-Archimedean local field is right adjoint to the parabolic induction functor for the opposite parabolic subgroup, in the generality of…

We characterize all pairs $(\mathcal{A}$,$\mathcal{B})$ of generalized Riemann differences for which $\mathcal{A}$-differentiability implies $\mathcal{B}$-differentiability. Two generalized Riemann derivatives $\mathcal{A}$ and…

Let $P,Q$ be standard parabolic subgroups of a $p$-adic reductive group $G$. We study the smooth dual of the filtration on a parabolically induced module arising from the geometric lemma associated to the cosets $P\setminus G/Q$. We prove…

We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an algebraic curve. Using principles of…

Polynomial representations of general linear groups and modules over Schur algebras are compared. We work over an arbitrary commutative ring and show that Schur-Weyl duality is the key for an equivalence between both categories.

We discuss the branching problem for generalized Verma modules $M_\lambda(\mathfrak g, \mathfrak p)$ applied to couples of reductive Lie algebras $\bar{\mathfrak g}\hookrightarrow \mathfrak g$. The analysis is based on projecting character…

We study the p-adic analogue of the arithmetic Gan-Gross-Prasad (GGP) conjectures for unitary groups. Let $\Pi$ be a conjugate-selfdual cuspidal automorphic representation of GL_{n} x GL_{n+1} over a CM field, which is algebraic of minimal…

We develop a framework for a duality theory for general multilinear operators which extends that for transversal multilinear operators which has been established in arXiv:1809.02449. We apply it to the setting of joints and multijoints, and…

Let q be a power of a prime and n a positive integer. Let P(q) be a parabolic subgroup of the finite general linear group GL(n,q). We show that the number of P(q)-conjugacy classes in GL(n,q) is, as a function of q, a polynomial in q with…

Bernstein blocks of complex representations of p-adic reductive groups have been computed in a large amount of examples, in part thanks to the theory of types a la Bushnell and Kutzko. The output of these purely representation-theoretic…

The quantum duality principal (QDP) by Drinfeld predicts a connection between the quantized universial enveloping algebras and the quantized coordinate algebras, where the underlying classical objects are related by the duality in Poisson…

In [7], results about the global Jacquet-Langlands correspondence, (weak and strong) multiplicity-one theorems and the classification of automorphic representations for inner forms of the general linear group over a number field are…

We consider two families of polynomials $\mathbb{P}=\polP$ and $\mathbb{Q}=\polQ$\footnote{Here and below we consider only monic polynomials.} orthogonal on the real line with respect to probability measures $\mu$ and $\nu$ respectively.…

We generalize the Galileon duality to any single scalar field Lagrangian coupled locally to any matter field. Under the duality, a generalized Galileon maps into another generalized Galileon via a one parameter group of transformations,…

In this paper we construct a generalization of the classical Steinberg section for the quotient map of a semisimple group with respect to the conjugation action. We then give various applications of our construction including the…

In this note we clarify the relationship between the local and global definitions of dual pairs in Poisson geometry. It turns out that these are not equivalent. For the passage from local to global one needs a connected fiber hypothesis…

Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…