Related papers: Some remarks on monogenity
Given a subgroup H of a finite group G, we begin a systematic study of the partial representations of G that restrict to global representations of H. After adapting several results from [DEP00] (which correspond to the case where H is…
This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.
We investigate the rate of growth of the function of n which counts the number of complex irreducible representations of a fixed group of degree less than or equal to n. The emphasis is on linear groups, especially compact real and p-adic…
We prove a new formula for the generating function of polynomials counting absolutely stable representations of quivers over finite fields. The case of irreducible representations is studied in more detail.
We simplify construction of Thoma representations of an infinite symmetric group
In a recent paper [Trans. Amer. Math. Soc. 378 (2025), 851-883], the concept of generalized partial-slice monogenic (or regular) function was introduced over Clifford algebras. The present paper shall extend the study of generalized…
Algebras of ultradifferentiable generalized functions are introduced. We give a microlocal analysis within these algebras related to the regularity type and the ultradifferentiable property.
For a residually finite group $G$, its normal subgroups $G\supset G_1\supset G_2\cdots$ with $\cap_{n\in\mathbb N}G_n=\{e\}$ and for a growth function $\gamma$ we construct a unitary representation $\pi_\gamma$ of $G$. For the minimal…
This work proposes a unified theory of regularity in one hypercomplex variable: the theory of $T$-regular functions. In the special case of quaternion-valued functions of one quaternionic variable, this unified theory comprises…
An elementary approach to the construction of Coxeter group representations is presented.
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
In this paper I explore the relationship between regular functions associated to local systems on nilpotent orbits and unipotent representations in the complex groups.
In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…
In this paper we offer a definition of monogenicity for functions defined on $\rr^{n+1}$ with values in the Clifford algebra $\rr_n$ following an idea inspired by the recent papers \cite{gs}, \cite{advances}. This new class of monogenic…
We study groups, exponential groups and ordered groups equipped with valuations. We investigate algebraic and topological features of such valued structures, and apply our findings in order to solve regular equations over groups using…
We discuss some basic properties of the Sibony functions and pseudometrics.
For any set representation (permutation representation) of the symmetric group $S_n$, we give combinatorial interpretation for coefficients of its Frobenius character expanded in the basis of monomial symmetric functions.
We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
In this work, we establish a representation theorem for multivariable totally symmetric functions: a multisymmetric continuous function must be the composition of a continuous function and a set of generators of the multisymmetric…