Related papers: Spin layer groups and their corepresentations

We classify non-polar irreducible representations of connected compact Lie groups whose orbit space is isometric to that of a representation of a finite extension of $Sp(1)^k$ for some $k>0$. It follows that they are obtained from isotropy…

In this work, we exhaust all the spin-space symmetries, which fully characterize collinear, non-collinear, commensurate, and incommensurate spiral magnetism, and investigate enriched features of electronic bands that respect these…

We introduce the symplectic group $\mathrm{Sp}_2(G, \sigma)$ associated to a Lie subgroup $G$ of a (possibly noncommutative) associative algebra $A$ equipped with an anti-involution $\sigma$. Our construction recovers several classical Lie…

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…

Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…

Tables of crystallographic properties of double antisymmetry space groups, including symmetry element diagrams, general position diagrams, and positions, with multiplicities, site symmetries, coordinates, spin and roto vectors are…

It is widely accepted that spin-orbit coupling (SOC) generally locks spin and spatial degrees of freedom, as a result, the spin, despite being an axial vector, is fixed and cannot rotate independently, and the magnetic system should be…

We investigate orthogonal representations of compact Lie groups from the point of view of their quotient spaces, considered as metric spaces. We study metric spaces which are simultaneously quotients of different representations and…

The Bondi-Metzner-Sachs group in three dimensions is the symmetry group of asymptotically flat three-dimensional spacetimes. It is the semi-direct product of the diffeomorphism group of the circle with the space of its adjoint…

Symmetry breaking together with strong spin-orbit interaction give rise to many exciting phenomena within condensed matter physics. A recent example is the existence of chiral spin textures, which are observed in magnetic systems lacking…

Recently, shearlet groups have received much attention in connection with shearlet transforms applied for orientation sensitive image analysis and restoration. The square integrable representations of the shearlet groups provide not only…

A concrete representation of the Clifford algebra (for any hyperbolic quadratic space) is given using what are called Suslin matrices. This explicit construction is used to analyze the corresponding Spin groups and the involution and might…

This paper investigates some actions "\`a la Johnson" on the set, denoted by ${\cal E}$, of Spin-structures which are interpreted as special double-coverings of a trivial $S^1-$fibration over a non-orientable surface $N_{g+1}$. The group…

We investigate 2-dimensional Viscoelastic equations with a view of Lie groups. In this sense, we answer question of the symmetry classification. We provide the algebra of symmetry and build the optimal system of Lie subalgebras. Reductions…

In this work we provide an elementary derivation of the indefinite spin groups in low-dimensions. Our approach relies on the isomorphism of Cl(p+1, q+1) to the algebra 2x2 matrices with entries in Cl(p,q), simple properties of Kronecker…

We relate the linear asymptotic representation theory of the symmetric groups to its spin counterpart. In particular, we give explicit formulas which express the normalized irreducible spin characters evaluated on a strict partition $\xi$…

We define a 3-generator algebra obtained by replacing the commutators by anticommutators in the defining relations of the angular momentum algebra. We show that integer spin representations are in one to one correspondence with those of the…

The past years have seen rapid progress in the classification of topological materials. These diagnostical methods are increasingly getting explored in the pertinent context of magnetic structures. We report on a general class of electronic…

We use low-depth quantum circuits, a specific type of tensor networks, to classify two-dimensional symmetry-protected topological many-body localized phases. For (anti-)unitary on-site symmetries we show that the (generalized) third…

A model invariant under a supersymmetric extension of the rotation group O(3) is mapped, using a stereographic projection, from the spherical surface S2 to two dimensional Euclidean space. The resulting model does not have a manifest local…