4 Conjectures and results 12 4.1 The symmetry conjecture . . . . . . . . . . . . . . . . . . . . . . 12 4.2 Othogonal idempotents and character formulas . . . . . . . . . . 15 4.3 The double coset conjecture . . . . . . . . . . . . . . . . . . . . . 17 4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.5 The case of a single generator . . . . . . . . . . . . . . ...

We address the question of supersymmetry breaking of a higher dimensional supersymmetric theory due to coset space dimensional reduction. In particular we study a ten-dimensional supersymmetric E8 gauge theory which is reduced over all six-dimensional coset spaces. We find that the original supersymmetry is completely broken in the process of dimensional reduction when the coset spaces are symm...

Inspired by Lie algebra expansion, we consider an extension of the introduced in A. Fontanella and S. J. van Tongeren [Coset space actions for nonrelativistic strings, High Energy Phys. 06 (2022) 80.] string coset action ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$. We show that extended admits a nondegenerate inner product which is adjoint invariant under full algebra...

Coset enumeration is one of the basic tools for investigating nitely presented groups. Many enumerations require signiicant resources, in terms of CPU time or memory space. We develop a fully functional parallel coset enumeration procedure and we discuss some of the issues involved in such parallelisation using the POSIX threads library. Our results can equally well be applied to any master-sla...