Related papers: Some questions about representations of p-adic gro…
This is an expository article on properties of actions on Lie groups by subgroups of their automorphism groups. After recalling various results on the structure of the automorphism groups, we discuss actions with dense orbits, invariant and…
In this short survey article, we try to list maximum number of known results on class preserving automorphisms of finite $p$-groups. We conclude the survey with some interesting (at least for the author) open problems on this topic.
We study finite groups which possess a strongly p-embedded subgroup for some odd prime p. The main results of the paper will be applied in the ongoing project to classify the simple groups of local characteristic p.
We investigate braid group representations associated with unitary braided vector spaces, focusing on a conjecture that such representations should have virtually abelian images in general and finite image provided the braiding has finite…
Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…
We develop the theory of $H$-graded manifolds for any finitely generated abelian group, using tools from representation theory. Furthermore, we introduce and investigate the notion of $H$-graded coverings of supermanifolds in the case where…
An analogue of the Gauss-Lucas theorem for polynomials over the algebraic closure $\mathbb C_p$ of the field of $p$-adic numbers is considered.
In \cite{Pillay} and more formally in \cite{Onshuus-Pillay} it was asked whether open subgroups of $p$-adic algebraic groups are ($p$-adic) semialgebraic, equivalently, definable in the structure $(\mathbb Q_{p}, +, \times)$. We give a…
We provide detailed calculations for the classification of representations of compact simple Lie groups with non-empty boundary in the orbit space, first announced in a previous paper [arXiv:2112.00513] by the same authors.
In this paper, we will study p-adic q-expansion of alternating sums of powers. From these properties, we derive some interesting properties related to p-adic q-expansion of alternating sums of powers
In this paper, we give a fermionic p-adic integral representions of Benstein polynomials associated with Euler numbers and polynomials. Finally, we give some interesting identities for the Euler numbers by using the properties of our…
In this paper, we study Catalan numbers which can be represented by the p-adic integral on Zp and we investigate some properties and formulae related to Catalan numbers and special numbers.
In this paper I present some open problems on Coxeter groups and unimodality, together with the main partial results, and computational evidence, that are known about them.
The purpose of this paper is to define a set of representations of Sp(p,q) and SO*(2n), the unipotent representations of the title, and establish their unitarity. The unipotent representations considered here properly contain the special…
We investigate the relation between p-adic Galois representations and overconvergent (phi,Gamma)-modules in families. Especially we construct a natural open subspace of a family of (phi,Gamma)-modules, over which it is induced by a family…
We study the representation theory of the increasing monoid. Our results provide a fairly comprehensive picture of the representation category: for example, we describe the Grothendieck group (including the effective cone), classify…
We investigate the braid group representations arising from categories of representations of twisted quantum doubles of finite groups. For these categories, we show that the resulting braid group representations always factor through finite…
The aim of the present paper is to provide a comprehensive introduction to some algebraic and geometric aspects of real representations of compact Lie groups, as well as some results concerning isotropy strata and restriction of invariants.
Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will…
Topological characterization of torus groups is given.