Related papers: Descent equalities and the inductive McKay conditi…

Necessary and sufficient conditions are presented for the (first-order) theory of a universal class of algebraic structures (algebras) to admit a model completion, extending a characterization provided by Wheeler. For varieties of algebras…

To study induced representation of some class of groups, Mackey's theory is very useful. In this paper, we consider some generalization of Mackey's theory for locally profinite groups. In particular, we give conditions on groups under which…

We prove a general theorem which allows the determination of Lie symmetries of Laplace equation in a general Riemannian space using the conformal group of the space. Algebraic computing is not necessary. We apply the theorem in the study of…

Let $P$ be a Sylow $p$-subgroup of a finite $p$-solvable group $G$, where $p$ is a prime. Using a normal $p$-series $\mathcal{N}$ of $G$, we introduce the notion of $(\mathcal{N},p)$-stable characters and prove that $G$ and ${\bf N}_G(P)$…

We provide a new proof of Ishii's conjecture for any dihedral reflection group $G\subset GL_2(\mathbb{C})$ from the viewpoint of Bridgeland stability conditions. Our strategy is to reduce the problem, via the derived McKay correspondence,…

A continuous-time particle system on the real line satisfying the branching property and an exponential integrability condition is called a branching L\'evy process, and its law is characterized by a triplet $(\sigma^2,a,\Lambda)$. We…

We establish the (non-lattice) local limit theorem for products of i.i.d. random variables on an arbitrary simply connected nilpotent Lie group $G$, where the variables are allowed to be non-centered. Our result also improves on the known…

This paper deals with sufficiency conditions for irreducibility of certain induced modules. We also construct irreducible representations for a group $G$ over a field ${\mathbb K}$ where the group $G$ is a semidirect product of a normal…

We solve the regularity problem for Milnor's infinite dimensional Lie groups in the $C^0$-topological context, and provide necessary and sufficient regularity conditions for the (standard) $C^k$-topological setting. We prove that the…

We study the Eisenstein ideal for modular forms of even weight $k>2$ and prime level $N$. We pay special attention to the phenomenon of $\mathit{extra \ reducibility}$: the Eisenstein ideal is strictly larger than the ideal cutting out…

This paper develops a new framework for indirect statistical inference with guaranteed necessity and sufficiency, applicable to continuous random variables. We prove that when comparing exponentially transformed order statistics from an…

We establish the inductive blockwise Alperin weight condition for simple groups of Lie type $\mathsf C$ and the bad prime $2$. As a main step, we derive a labelling set for the irreducible $2$-Brauer characters of the finite symplectic…

Measure contraction properties are generalizations of the notion of Ricci curvature lower bounds in Riemannian geometry to more general metric measure spaces. In this paper, we give sufficient conditions for a Sasakian manifold equipped…

The original Lawvere condition asserts that every reflexive graph admits a unique natural structure of internal groupoid. This property was identified by P. T. Johnstone, following a question by A. Carboni and a suggestion by F. W. Lawvere,…

We introduce the notion of $\mathbb{E}_\infty$-descendability as well as a derived variant. We prove that several classes of descendable maps of commutative rings are $\mathbb{E}_\infty$-descendable. As an application, we prove a variant of…

The aim of this article is to refine a weak invariance principle for stationary sequences given by Doukhan & Louhichi (1999). Since our conditions are not causal our assumptions need to be stronger than the mixing and causal $\theta$-weak…

In this paper, we propose a new interpretation of local limit theorems for univariate and multivariate distributions on lattices. We show that - given a local limit theorem in the standard sense - the distributions are approximated well by…

In the paper "Einstein metrics on compact simple Lie groups attached to standard triples", the authors introduced the definition of standard triples and proved that every compact simple Lie group $G$ attached to a standard triple $(G,K,H)$…

The paper provides a simple test for deciding, from a given causal diagram, whether two sets of variables have the same bias-reducing potential under adjustment. The test requires that one of the following two conditions holds: either (1)…

Previous formulations of group theory in ACL2 and Nqthm, based on either "encapsulate" or "defn-sk", have been limited by their failure to provide a path to proof by induction on the order of a group, which is required for most interesting…