Related papers: Character Levels and Character Bounds. II

We analyse some aspects of the notion of algebraic exponentiation introduced by the second author [16] and satisfied by the category of groups. We show how this notion provides a new approach to the categorical-algebraic question of the…

We initiate the study of finite characterizations and exact learnability of modal languages. A finite characterization of a modal formula w.r.t. a set of formulas is a finite set of finite models (labelled either positive or negative) which…

In this paper, we consider covers of finite groups by centralizers of elements. We show that the set of centralizers that are maximal under the partial ordering form a cover of the group. We also show that the set of centralizers that are…

We give a lower bound for the sup-norm of an $L^2$-normalized newform in an irreducible, unitary, cuspidal representation $\pi$ of $GL_2$ over a number field. When the central character of $\pi$ is sufficiently ramified, this bound improves…

Given a characteristic, we define a character of the Siegel modular group of level 2, the computations of their values are also obtained. By using our theorems, some key theorems of Igusa [1] can be recovered.

Berkovich, Chillag and Herzog characterized all finite groups $G$ in which all the nonlinear irreducible characters of $G$ have distinct degrees. In this paper we extend this result showing that a similar characterization holds for all…

In this paper we study higher level Deligne--Lusztig representations of reductive groups over discrete valuation rings, with finite residue field $\mathbb{F}_q$. In previous work we proved that, at even levels, these geometrically…

Turull has described the fields of values for characters of $SL_n(q)$ in terms of the parametrization of the characters of $GL_n(q)$. In this article, we extend these results to the case of $SU_n(q)$.

The goal of this paper is to unify two lines in a particular area of graph limits. First, we generalize and provide unified treatment of various graph limit concepts by means of a combination of model theory and analysis. Then, as an…

Let $G$ be a reductive group defined over a number field. Denote $Z(\hat G)$ the center of the dual group. Langlands has defined some homomorphism from some cohomology group of $Z(\hat G)$ into the group of automorphic characters of $G$. We…

Let $p$ be a an odd prime and let $G$ be a finite $p$-group with cyclic commutator subgroup $G'$. We prove that the exponent and the abelianization of the centralizer of $G'$ in $G$ are determined by the group algebra of $G$ over any field…

We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…

For a variety of finite groups $\mathbf H$, let $\overline{\mathbf H}$ denote the variety of finite semigroups all of whose subgroups lie in $\mathbf H$. We give a characterization of the subsets of a finite semigroup that are pointlike…

We answer in the negative a question of Hartley about representations of finite groups, by constructing examples of finite simple groups with arbitrarily large representations whose endomorphism ring consists of just the scalars. We show as…

We extend to the critical (intermediate) regularity several results concerning rigidity for centralizers and group actions on the interval.

For the class of solvable groups of homeomorphisms of the line preserving orientation and containing a freely acting element, we establish the metabelianity of the quotient group $G/H_G$, where the elements of the normal subgroup $H_G$ are…

We consider the lattice of supercharacter theories, in the sense of Diaconis and Isaacs, of the cyclic group of order n. We find necessary and sufficient conditions on n for that lattice to be upper or lower semimodular.

Minimizers in the least gradient problem with discontinuous boundary data need not be unique. However, all of them have a similar structure of level sets. Here, we give a full characterization of the set of minimizers in terms of any one of…

The classical It\^o-Michler theorem on character degrees of finite groups asserts that if the degree of every complex irreducible character of a finite group $G$ is coprime to a given prime $p$, then $G$ has a normal Sylow $p$-subgroup. We…

This is the first installment of an exposition of an ACL2 formalization of elementary linear algebra, focusing on aspects of the subject that apply to matrices over an arbitrary commutative ring with identity, in anticipation of a future…