Related papers: Eichler orders, trees and Representation Fields

On smooth projective varieties of dimension $d$, $d$-tilting bundles are important in both geometry and representation theory, since they provide a bridge from the geometry of such varieties to the derived McKay correspondence and to higher…

We classify finite dimensional simple spherical representations of rational double affine Hecke algebras, and we study a remarkable family of finite dimensional simple spherical representations of double affine Hecke algebras.

We describe the set of maximal orders in a 2-by-2 matrix algebra over a non-commutative local division algebra B containing a given suborder, for certain important families of such suborders, including rings of integers of division…

We consider maximal non-$l$-intertwining collections, which are a higher-dimensional version of the maximal non-crossing collections which give clusters of Pl\"ucker coordinates in the Grassmannian coordinate ring, as described by Scott. We…

This is the first in a series of papers on type I Howe duality for finite fields, concerning the restriction of an oscillator representation of the symplectic group to a product of a symplectic and an orthogonal group. The goal of the…

Motivated by the Lawrence-Krammer-Bigelow representations of the classical braid groups, we study the homology of unordered configurations in an orientable genus-$g$ surface with one boundary component, over non-commutative local systems…

Calculational tools are provided allowing to determine general tree-level scattering amplitudes for processes involving bosons and fermions in heterotic and superstring theories in four space-time dimensions. We compute higher-point…

The class in the Brauer group of a quaternion algebra over a field is 2-torsion. We study the following question: Which 2-torsion elements of the Brauer group of a complex function field are representable by quaternion algebras? Using…

This note is devoted to the study of families of quaternionic modular forms arising from orders defined by Pizer. In this situation, the Hecke-eigenspaces are 2-dimensional contrary to the classical case of Eichler orders. The main result…

We study two general approaches how to describe spin one particles, using vector and antisymmetric tensor fields within RChT. In this paper we focus on the question of an equivalence of both ways. The appearing problems lead us to the…

A number of first-order calculi employ an explicit model representation formalism for automated reasoning and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of…

This paper surveys the representation theory of rational Cherednik algebras. We also discuss the representations of the spherical subalgebras. We describe in particular the results on category O. For type A, we explain relations with the…

Let $K$ be a global function field together with a place $\infty$, and $A$ the subring of functions regular outside $\infty$. In this paper we present an effective method to evaluate the (locally free) class number of an arbitrary…

We discuss algebraic and representation theoretic structures in braided tensor categories C which obey certain finiteness conditions. Much interesting structure of such a category is encoded in a Hopf algebra H in C. In particular, the Hopf…

For every positive integer h, the representation function of order h associated to a subset A of the integers or, more generally, of any group or semigroup X, counts the number of ways an element of X can be written as the sum (or product,…

We prove that for every ordered abelian group $G$ there exists a non-trivial ordered abelian group $H$ such that $G\preccurlyeq H\oplus G$ with the lexicographic order, and give a first-order characterization of ordered abelian group $G$…

We study subclasses of grid intersection graphs from the perspective of order dimension. We show that partial orders of height two whose comparability graph is a grid intersection graph have order dimension at most four. Starting from this…

We establish a fundamental theorem of orders (FTO) which allows us to express all orders uniquely as an intersection of `irreducible orders' along which the index and the conductor distributes multiplicatively. We define a subclass of…

This paper contributes to the theory of orders of number fields. This paper defines a notion of "ray class group" associated to an arbitrary order in a number field together with an arbitrary ray class modulus for that order (including…

We consider a finite fields version of the Erd\H{o}s-Falconer distance problem for two different sets. In a certain range for the sizes of the two sets we obtain results of the conjectured order of magnitude.