相关论文: On tolerances representable as $R \circ R^-$
In this article we give two different ways of representations of circular words. Representations with tuples are intended as a compact notation, while representations with trees give a way to easily process all conjugates of a word. The…
We provide several characterizations of ring-shaped rotationally symmetric solutions to the Serrin problem in arbitrary dimensions.
In the space of orientation-preserving circle maps that are not necessarily surjective nor injective, the rotation number does not vary continuously. Each map where one of these discontinuities occurs is itself discontinuous and we can…
Actual individual preferences are neither complete (=total) nor antisymmetric in general, so that at least every quasi-order must be an admissible input to a satisfactory choice rule. It is argued that the traditional notion of…
Given a reflection group $G$ acting on a complex vector space $V$, a reflection map is the composition of an embedding $X \hookrightarrow V$ with the orbit map $V\to\mathbb C^p$ that maps a $G$-orbit to a point. Reflection maps can be very…
We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, spaces of representations of quivers, and on…
We show that if $\{\rho_{\ell}\}$ is a compatible system of absolutely irreducible Galois representations of a number field then the residual representation $\overline{\rho}_{\ell}$ is absolutely irreducible for $\ell$ in a density 1 set of…
The category of admissible (in the appropriately modified sense of representation theory of totally disconnected groups) semi-linear representations of the automorphism group of an algebraically closed extension of infinite transcendence…
Argumentation is a promising model for reasoning with uncertain knowledge. The key concept of acceptability enables to differentiate arguments and counterarguments: The certainty of a proposition can then be evaluated through the most…
We construct examples of two convex bodies $K,L$ in $\mathbb{R}^n$, such that every projection of $K$ onto a $(n-1)$-dimensional subspace can be rotated to be contained in the corresponding projection of $L$, but $K$ itself cannot be…
The concept of a tolerance relation, shortly called tolerance, was studied on various algebras since the seventieth of the twentieth century by B. Zelinka and the first author. Since tolerances need not be transitive, their blocks may…
We study generic representations of general linear groups over a finite ring R with coefficients in a field k in which the cardinality of R is invertible, that is functors from finitely-generated projective R-modules to k-vector spaces. We…
The paper extends existing Lie algebra representation theory related to Lie algebra gradings. The notion of a representation compatible with a given grading is defined and applied to finite-dimensional representations of $sl(n,\mathbb{C})$…
In this paper we study certain category of smooth modules for reductive $p$--adic groups analogous to the usual smooth complex representations but with the field of complex numbers replaced by a $\mathbb Q$--algebra. We prove some…
This work presents code to procedurally generate examples for the ARC training tasks. For each of the 400 tasks, an example generator following the transformation logic of the original examples was created. In effect, the assumed underlying…
The main result of the paper is a reciprocity law which proves that compatible systems of semisimple, abelian mod $p$ representations (of arbitrary dimension) of absolute Galois groups of number fields, arise from Hecke characters. In the…
The paper contained a preliminary version of a general theory of reciprocity laws on vector spaces.
There has been some work in the literature on limit theorems for the trace of commutators for compact Lie groups. We revisit this from the perspective of combinatorial representation theory.
A description of an algorithm for a rather general modal grating calculation is presented. Arbitrary profiles, depth, and permittivity are allowed. Gratings built up from sub-gratings are allowed, as are coatings on the sidewalls of lines,…
In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…