A classification of four-tuples of spinors of a ten dimensional space

2025/12/22 by Willem A. de Graaf, de Graaf, Willem, A. G. Élashvili +3
Mathematics · #17B10 #22E46 #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2512.19257

openalex publication_date 2025/12/22 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28

Abstract

We use the theory of theta-groups developed by Vinberg, along with computations in the computer algebra system GAP4, to classify the orbits of Spin(10,C)x SL(4,C) acting on the tensor product of the half spin module of Spin(10,C) and the natural module of SL(4,C).

Citations

• On linear sections of the spinor tenfold II
• A Translation of "Classification of four-vectors of an 8-dimensional space," by Antonyan, L. V. , with an appendix by the translator
• An effective method to compute closure ordering for nilpotent orbits of θ-representations
• Computing representatives of nilpotent orbits of theta-groups

Related

• Notes on spinors in low dimension
• Finslerian N-spinors: Algebra
• Spinors from pure spinors
• Part I: Vector Analysis of Spinors
• Geometry of Spin(10) Symmetry Breaking