相关论文: Exterior-Model Spinors in Split Rank: Exact Levi I…

Let $H^*(\calB_e)$ be the cohomology of the Springer fibre for the nilpotent element $e$ in a simple Lie algebra $\g$, on which the Weyl group $W$ acts by the Springer representation. Let $\Lambda^i V$ denote the $i$th exterior power of the…

A geometric approach to the standard model in terms of the Clifford algebra Cl_7 is advanced. A key feature of the model is its use of an algebraic spinor for one generation of leptons and quarks. Spinor transformations separate into…

We develop the theory of spinorial polyforms associated with bundles of irreducible Clifford modules of non-simple real type, obtaining a precise characterization of the square of an irreducible real spinor in signature $(p-q) =…

The fermionic fields of one generation of the Standard Model, including the Lorentz spinor degrees of freedom, can be identified with components of a single real 64-dimensional semi-spinor representation S of the group Spin(11,3). We…

Results on symplectic spinors and their higher spin versions, concerning representation theory and cohomology properties are presented. Exterior forms with values in the symplectic spinors are decomposed into irreducible modules including…

Recent papers by Markman and O'Grady give, besides their main results on the Hodge conjecture and on hyperkaehler varieties, surprising and explicit descriptions of families of abelian fourfolds of Weil type with trivial discriminant. They…

Higgs multiplet in the vector-spinor representations of SO(10), i.e., the $144+\bar{144}$ multiplet can break the SO(10) gauge symmetry spontaneously in one step down to the Standard Model gauge group symmetry $SU(3)_C\times SU(2)_L\times…

In the context of supersymmetric $SO(10)$ grand unified models, it is shown that the gauge symmetry breaking as well as a natural doublet--triplet splitting can be achieved with a minimal Higgs system consisting of a single adjoint and a…

We develop the differential theory of complex spinorial forms associated with irreducible complex spinors across all dimensions and signatures. This framework enables the study of constrained parallelicity conditions for irreducible complex…

Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It…

Contrary to what is sometimes stated, the current electroweak precision data easily allow for massive composite resonance states at the natural EW scale, i.e., well over the TeV. The oblique parameters S and T are analyzed by means of an…

This paper is intended to describe twistors via the paravector model of Clifford algebras and to relate such description to conformal maps in the Clifford algebra over R(4,1), besides pointing out some applications of the pure spinor…

Let $F$ be a local non-Archimedean field and $E$ a finite Galois extension of $F$, with Galois group $G$. If $\rho$ is a representation of $G$ on a complex vector space $V$, we may compose it with any tensor operation $R$ on $V$, and get…

We study the eigenvalue problem of the squared Pauli-Lubanski vector, W^{2}, in the Spinor-Vector representation space and derive from it that the -s(s+1)m^{2} subspace with s=3/2, i.e. spin 3/2 in the rest frame, is pinned down by the one…

We incorporate Sogami's idea in the standard model into our previous formulation of non-commutative differential geometry by extending the action of the extra exterior derivative operator on spinors defined over the discrete space-time;…

Let $K$ be a 2-dimensional global field of characteristic $\neq 2$, and let $V$ be a divisorial set of places of $K$. We show that for a given $n \geqslant 5$, the set of $K$-isomorphism classes of spinor groups $G = \mathrm{Spin}_n(q)$ of…

Hypercubic groups in any dimension are defined and their conjugate classifications and representation theories are derived. Double group and spinor representation are introduced. A detailed calculation is carried out on the structures of…

Consider an asymptotically Euclidean initial data set with a smooth marginally trapped surface (possibly a union of future and past multi-connected components) as inner boundary. By a further development of the spinorial framework…

We investigate the differential geometry and topology of globally hyperbolic four-manifolds $(M,g)$ admitting a parallel real spinor $\varepsilon$. Using the theory of parabolic pairs recently introduced in arXiv:1911.08658 , we first…

Starting from the general concept of a Lie derivative of an arbitrary differentiable map, we develop a systematic theory of Lie differentiation in the framework of reductive G-structures P on a principal bundle Q. It is shown that these…