Related papers: Enumeration and representation theory of spin spac…
Magnetic structures of the noncentrosymmetric magnet Sr$_2$MnSi$_2$O$_7$ were examined through neutron diffraction for powder and single-crystalline samples, as well as magnetometry measurements. All allowed magnetic structures under the…
For over 100 years, the group-theoretic characterization of crystalline solids has provided the foundational language for diverse problems in physics and chemistry. However, the group theory of crystals with commensurate magnetic order has…
The representation theory of the symmetric groups is intimately related to geometry, algebraic combinatorics, and Lie theory. The spin representation theory of the symmetric groups was originally developed by Schur. In these lecture notes,…
Two-dimensional unconventional magnetism has recently attracted growing interest due to its intriguing physical properties and promising applications in spintronics. However, existing studies on stacking-induced unconventional magnetism…
We show that all spin groups of non-definite, quinary quadratic forms over a field with characteristic 0 can be represented as 2 by 2 matrices with entries in an associated quaternion algebra. Over local and global fields, we further study…
We introduce a classification of the radial spin textures in momentum space that emerge at high-symmetry points in crystals characterized by non-polar chiral point groups ($D_2$, $D_3$, $D_4$, $D_6$, $T$, $O$). Based on the symmetry…
Materials with interesting physical properties are often designed based on our understanding of the target physical effects. The physical properties can be either explicitly observed ("apparent") or concealed by the perceived symmetry…
In a space of $d=15 $ Grassmann coordinates, two types of generators of the Lorentz transformations, one of spinorial and the other of vectorial character, both linear operators in Grassmann space, forming the group $ SO(1,14) $ which…
The monograph offers a coherent and self-contained treatment of massless (ladder) representations of the conformal group U(2,2) and their restriction to the de Sitter group Sp(2,2), combining rigorous representation-theoretic analysis with…
The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…
We present a systematic classification of emergent particles in all 528 magnetic layer groups and 394 magnetic rod groups, which describe two-dimensional and one-dimensional crystals respectively. Our approach is via constructing a…
The canonical quantisation of General Relativity including matter on a spacetime manifold in the globally hyperbolic setting involves in particular the representation theory of the spatial diffeomorphism group (SDG), and/or its Lie algebra…
Properties of a given symmetry group G are very important in investigation of a physical system invariant under its action. In the case of finite spin systems (magnetic rings, some planar macromolecules) the symmetry group is isomorphic…
The representation theory of tensor functions is essential to constitutive modeling of materials including both mechanical and physical behaviors. Generally, material symmetry is incorporated in the tensor functions through a structural or…
This article is a write-up of the talk given in one of the mini-symposia of the 2024 European Congress of Mathematicians. I will explain some basics of the representation theory underlying Spin(10) and SU(5) Grand Unified Theories. I will…
In three-dimensional (3D) crystals, emergent particles arise when two or multiple bands contact and form degeneracy (band crossing) in the Brillouin zone. Recently a complete classification of emergent particles in 3D nonmagnetic crystals,…
There are two well-known ways of describing elements of the rotation group SO$(m)$. First, according to the Cartan-Dieudonn\'e theorem, every rotation matrix can be written as an even number of reflections. And second, they can also be…
Magnetic order is a fundamental property of materials, governing collective behavior and enabling a broad range of functionalities. Yet magnetic structure remains difficult to determine: experiments are costly and specialized, while…
A group theoretical description of basic discrete symmetries (space inversion P, time reversal T and charge conjugation C) is given. Discrete subgroups of orthogonal groups of multidimensional spaces over the fields of real and complex…
We propose a new classification of magnetic textures from the viewpoint of differential geometry. Magnetic textures are conventionally classified into collinear, coplanar, and noncoplanar magnets. These classes are typically characterized…