Diode effects are of great interest for both fundamental physics and modern technologies. Electrical diode effects (nonreciprocal transport) have been observed in Weyl systems. Optical diode effects arising from the Weyl fermions have been theoretically co ...
Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional ir ...
The arise of disagreement is an emergent phenomenon that can be observed within a growing social group and, beyond a certain threshold, can lead to group fragmentation. To better understand how disagreement emerges, we introduce an analytically tractable m ...
Let G be a simple algebraic group over an algebraically closed field F of characteristic p >= h, the Coxeter number of G. We observe an easy 'recursion formula' for computing the Jantzen sum formula of a Weyl module with p-regular highest weight. We also d ...
We generalize the fixed-point property for discrete groups acting on convex cones given by Monod in [23] to topological groups. At first, we focus on describing this fixed-point property from a functional point of view, and then we look at the class of gro ...
We start this short note by introducing two remarkable mathematical objects: the E8E8 root lattice Lambda8Lambda8 in 8-dimensional Euclidean space and the Leech lattice Lambda24Lambda24 in 24-dimensional space. These two lattices stand out among their lat ...
We study the spectra of non-regular semisimple elements in irreducible representations of simple algebraic groups. More precisely, we prove that if G is a simply connected simple linear algebraic group and φ : G → GL(V ) is a non-trivial irreducible repres ...
We study actions of groups by orientation preserving homeomorphisms on R (or an interval) that are minimal, have solvable germs at +/-infinity and contain a pair of elements of a certain dynamical type. We call such actions coherent. We establish that such ...
We show that for a large class C of finitely generated groups of orientation preserving homeomorphisms of the real line, the following holds: Given a group G of rank k in C, there is a sequence of k-markings (G,S-n), n is an element of N whose limit in the ...
Given a group Gamma, we establish a connection between the unitarisability of its uniformly bounded representations and the asymptotic behaviour of the isoperimetric constants of Cayley graphs of Gamma for increasingly large generating sets. The connection ...
Weyl semimetals such as the TaAs family (TaAs, TaP, NbAs, NbP) host quasiparticle excitations resemblingthe long-sought-after Weyl fermions at special band-crossing points in the band structure denoted as Weylnodes. They are predicted to exhibit a negative ...
In a number of cases the minimal polynomials of the images of unipotent elements of non-prime order in irreducible representations of the exceptional algebraic groups in good characteristics are found. It is proved that if p > 5 for a group of type E-8 and ...
Let G be the homeomorphism group of a dendrite. We study the normal subgroups of G. For instance, there are uncountably many nonisomorphic such groups G that are simple groups. Moreover, these groups can be chosen so that any isometric G-action on any metr ...
Let be a simple exceptional algebraic group of adjoint type over an algebraically closed field of characteristic and let be a subgroup of containing a regular unipotent element of . By a theorem of Testerman, is contained in a connected subgroup of of type ...
We construct a finitely presented, infinite, simple group that acts by homeomorphisms on the circle, but does not admit a non-trivial action by C1-diffeomorphisms on the circle. This is the first such example. The group emerges as a group of piecewise proj ...
Spectroscopic detection of Dirac and Weyl fermions in real materials is vital for both, promising applications and fundamental bridge between high-energy and condensed-matter physics. While the presence of Dirac and noncentrosymmetric Weyl fermions is well ...
Online services are becoming more and more ubiquitous and keep growing in scale. At the same time, they are required to be highly available, secure, energy-efficient, and to achieve high performance. To ensure these (and many other) properties, replication ...
We define and study in terms of integral Iwahoriâ Hecke algebras a new class of geometric operators acting on the Bruhat-Tits building of connected reductive groups over p-adic fields. These operators, which we call U-operators, generalize the geometric n ...
We construct examples of finitely generated infinite simple groups of homeomorphisms of the real line. Equivalently, these are examples of finitely generated simple left (or right) orderable groups. This answers a well known open question of Rhemtulla from ...
We establish obstructions for groups to act by homeomorphisms on dendrites. For instance, lattices in higher rank simple Lie groups will always fix a point or a pair. The same holds for irreducible lattices in products of connected groups. Further results ...
