Related papers: Soft bounds for local triple products and the subc…
The aim of this note is to point out a convexity property with respect to the root lattice for the support of the highest weights that occur in a tensor product of irreducible rational representations of $SL(n)$ over the complex numbers.…
We give a simple proof about the topological rigidity of closures of certain sparse unipotent orbits in $G/\Gamma$ where $G=\prod_{i=1}^k\operatorname{SL}_2(\mathbb R)$ and $\Gamma$ is an irreducible lattice in $G$.
Given a convergence theorem in analysis, under very general conditions a model-theoretic compactness argument implies that there is a uniform bound on the rate of metastability. We illustrate with three examples from ergodic theory.
We show that for all finite fields F_q, there exists a curve C over F_q of genus 3 such that the number of rational points on C is within 3 of the Serre-Weil upper or lower bound. For some q, we also obtain improvements on the upper bound…
In this paper, we establish the local converse theorem and the stability of local gamma factors for $\Mp_{2n}$ via the precise local theta correspondence between $\Mp_{2n}$ and $\SO_{2n+1}$ over local fields of characteristic not equal to…
We show that every admissible irreducible representation of a product of two locally compact groups is a tensor product of admissible irreducible representations of the factors.
Homogeneous power counting in Non-Relativistic QCD (NRQCD) implies the simultaneous existence of both soft and ultrasoft gluons. In the velocity renormalization group (vNRQCD) formalism we show that operators involving soft fields…
Let $V, W$ be finite-dimensional orthogonal representations of a finite group $G$. The equivariant degree with values in the Burnside ring of $G$ has been studied extensively by many authors. We present a short proof of the degree product…
In this paper, we study stable ergodicity of the action of groups of diffeomorphisms on smooth manifolds. Such actions are known to exist only on one-dimensional manifolds. The aim of this paper is to introduce a geometric method to…
Consider a sequence of finite regular graphs (GN) converging, in the sense of Benjamini-Schramm, to the infinite regular tree. We study the induced quantum graphs with equilateral edge lengths, Kirchhoff conditions (possibly with a non-zero…
We present a general formalism for deriving bounds on the shape parameters of the weak and electromagnetic form factors using as input correlators calculated from perturbative QCD, and exploiting analyticity and unitarity. The values…
We derive a tight and saturable monogamy relation for three-qubit pure states that bounds the sum of concurrence and concurrence of assistance by the entanglement with an external qubit. The bound decreases strictly with increasing external…
In this short note, we compute higher extension groups for all irreducible representations and deduce the multiplicity formula for finite length representations in triple product case.
Previous work of the second author and Wolf showed that given a set $A\subseteq \mathbb{F}_p^n$ of bounded $\textrm{VC}_2$-dimension, there is a high rank quadratic factor $\mathcal{B}$ of bounded complexity such that $A$ is approximately…
We consider elliptic equations of order $2m$ in a bounded domain $Q\subset\mathbb R^n$ with nonlocal boundary-value conditions connecting the values of a solution and its derivatives on $(n-1)$-dimensional smooth manifolds $\Gamma_i$ with…
In this paper we prove the Hodge conjecture for products of the form $S_1 \times ... S_n$, where $S_i$ are smooth projective surfaces such that $p_g(S_i)=1, q(S_i)=2$. We also prove the Hodge conjecture for arbitrary self-products of a K3…
We study a refinement of the quantum unique ergodicity conjecture for shrinking balls on arithmetic hyperbolic manifolds, with a focus on dimensions $ 2 $ and $ 3 $. For the Eisenstein series for the modular surface $\mathrm{PSL}_2(…
On a family of arithmetic hyperbolic 3-manifolds of squarefree level, we prove an upper bound for the sup-norm of Hecke-Maass cusp forms, with a power saving over the local geometric bound simultaneously in the Laplacian eigenvalue and the…
We study Gelfand pairs for locally compact quantum groups. We give an operator algebraic interpretation and show that the quantum Plancherel transformation restricts to a spherical Plancherel transformation. As an example, we turn the…
In this paper, we prove the conjectured order lower bound for the $k$-th moment of central values of quadratic twisted self-dual $\textrm{GL}(3)$ $L$-functions for all $k\geq 1$, based on our recent work on the twisted first moment of…