Related papers: Degree Differences in the Eta Correspondences
Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. We give an introduction focusing on the example of unitary groups and highlight…
In the context of infinity categories, we rethink the notion of derived functor in terms of correspondences. This is especially convenient for the description of a passage from an adjoint pair (F,G) of functors to a derived adjoint pair…
A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commu-tative ring. A main tool for this study is the construction of a correspondence functor associated…
We prove a universal property for the $(\infty, n)$-category of correspondences, generalizing and providing a new proof for the case $n = 2$ from [GR17]. We also provide conditions under which a functor out of a higher category of…
Let $K$ be an algebraically closed field of characteristic different from $2$. We provide a positive solution to the Bahturin--Regev conjecture in the general finite-dimensional (non-graded) setting, assuming that $\operatorname{char}(K)$…
We prove that $\delta$-derivations of a simple finite-dimensional Lie algebra over a field of characteristic zero, with values in a finite-dimensional module, are either inner derivations, or, in the case of adjoint module, multiplications…
Refereed version to appear on Journal of Algebraic Geometry. Unchanged content. Strongly ameliorated presentation thanks to referee's action.
A matrix $T \in \M_n(\C)$ is \emph{UECSM} if it is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. We develop several techniques for studying this property in dimensions three and four. Among other things, we…
The formal degree conjecture relates the formal degree of an irreducible square-integrable representation of a reductive group over a local field to the special value of the adjoint $\gamma$-factor of its $L$-parameter. In this paper, we…
The degree of a polynomial representing (or approximating) a function f is a lower bound for the number of quantum queries needed to compute f. This observation has been a source of many lower bounds on quantum algorithms. It has been an…
In this paper we develop a technique of computation of correlation functions in theories with action being cubic or higher degree form in terms of discriminants of corresponding tensors. These are analogues of formula $\int \exp…
A \emph{composition} is a sequence of positive integers, called \emph{parts}, having a fixed sum. By an \emph{$m$-congruence succession}, we will mean a pair of adjacent parts $x$ and $y$ within a composition such that $x\equiv y(\text{mod}…
The notion of double coset for semisimple finite dimensional Hopf algebras is introduced. This is done by considering an equivalence relation on the set of irreducible characters of the dual Hopf algebra. As an application formulae for the…
We prove that if two germs of irreducible complex analytic curves at $0\in\mathbb{C}^2$ have different sequence of characteristic exponents, then there exists $0<\alpha<1$ such that those germs are not $\alpha$-H\"older homeomorphic. For…
Riccati's differential equation is formulated as abstract equation in finite or infinite dimensional Banach spaces. Since the Riccati's differential equation with the Cole-Hopf transform shows a relation between the first order evolution…
The Gauge/Bethe correspondence of Nekrasov and Shatashvili relates the spectrum of integrable spin chains to the ground states of supersymmetric gauge theories. Up to now, this correspondence has been an observation; the underlying reason…
This is the first in a series of papers that deals with duality statements such as Mukai-duality (T-duality, from algebraic geometry) and the Baum-Connes conjecture (from operator $K$-theory). These dualities are expressed in terms of…
Given a fractional differential equation of order $\alpha \in (0,1]$ with Caputo derivatives, we investigate in a quantitative sense how the associated solutions depend on their respective initial conditions. Specifically, we look at two…
In this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains, with a special emphasis for the case when the ratio between these coefficients is large. In the most part of the work,…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…