Related papers: A criterion for the inductive Alperin weight condi…
In this note, we provide a different proof of Hill's criterion of freeness for abelian groups. Our proof hinges on the construction of suitable families of subgroups of the links in Hill's theorem and, ultimately, on the construction of…
Subject to a range of side conditions, the two weight inequality for the Hilbert transform is characterized in terms of (1) a Poisson A_2 condition on the weights (2) A forward testing condition, in which the two weight inequality is tested…
By using a novel technique that establishes a correspondence between general relativity and metric-affine theories based on the Ricci tensor, we are able to set stringent constraints on the free parameter of Born-Infeld gravity from the…
The McKay--Navarro conjecture is a refinement of the McKay conjecture that additionally takes the action of some Galois automorphisms into account. We verify the inductive McKay--Navarro condition in the defining characteristic for the…
We prove many cases of a conjecture of Buzzard, Diamond and Jarvis on the possible weights of mod $p$ Hilbert modular forms, by making use of modularity lifting theorems and computations in $p$-adic Hodge theory.
The paper studies weak Paley-Wiener properties for group extensions by use of Mackey's theory. The main theorem establishes sufficient conditions on the dual action to ensure that the group has the weak Paley-Wiener property. The theorem…
This paper introduces and studies the basic properties of Clifford algebra valued conditional measures.
We begin an investigation into extending the T1 theorem of David and Journ\'e, and the corresponding cancellation conditions of Stein, to more general pairs of distinct doubling weights. For example, assuming the measures satisfy a…
We complete the proof of the McKay--Navarro conjecture (also known as the Galois--McKay conjecture) for the prime 2, by completing the proof of the inductive McKay--Navarro conditions introduced by Navarro--Sp\"ath--Vallejo in this…
The weak boundedness property associated with a standard alpha-fractional Calderon-Zygmund operator and a weight pair is good-lambda controlled by the testing conditions and the Muckenhoupt and energy side conditions. As a consequence,…
The Littlewood-Richardson coefficients describe the decomposition of tensor products of irreducible representations of a simple Lie algebra into irreducibles. Assuming the number of factors is large, one gets a measure on the space of…
We extend the notion of Clifford index to reduced curves with planar singularities by considering rank 1 torsion free sheaves. We investigate the behaviour of the Clifford index with respect to the combinatorial properties of the curve and…
In this paper, we prove that a refinement of the Alperin-McKay Conjecture for $p$-blocks of finite groups, formulated by I. M. Isaacs and G. Navarro in 2002, holds for all covering groups of the symmetric and alternating groups, whenever…
The method of using rearrangements to give sufficient conditions for Fourier inequalities between weighted Lebesgue spaces is revisited. New results in the case q < p are established and a comparison between two known sufficient conditions…
The so-called "local-global" conjectures in the representation theory of finite groups relate the representation theory of $G$ to that of certain proper subgroups, such as the normalizers of particular $p$-groups. Recent results by several…
We obtain inductive and enumerative formulas for the multiplicities of the weights of the spin module for the Clifford algebra of a Levi subalgebra in a complex semisimple Lie algebra. Our formulas involve only matrices and tableaux, and…
This paper continues the investigation begun in arXiv:1906.05602 of extending the T1 theorem of David and Journ\'e, and optimal cancellation conditions, to more general weight pairs. The main additional tool developed here is a two weight…
A proof of Thompson's conjecture for real semi-simple Lie groups has been given by Kapovich, Millson, and Leeb. In this note, we give another proof of the conjecture by using a theorem of Alekseev, Meinrenken, and Woodward from symplectic…
For each prime $p$ and each positive integer $d$, we construct the first examples of second countable, topologically simple, $p$-adic Lie groups of dimension $d$ whose Lie algebras are abelian. This answers several questions of Gl\"ockner…
Let $k > 3$ be an integer and $p$ a prime with $p > 2k-2$. Let $f$ be a newform of weight $2k-2$ and level 1 so that $f$ is ordinary at $p$ and $\bar{\rho}_{f}$ is irreducible. Under some additional hypotheses we prove that…