PreprintThe spinor norm and homomorphism algorithms for classical groupsScott H. Murray, Colva M. RoneyDougalAbstractWe investigate the structure of the normaliser N in GLd(q) of the orthogonal omega group. We develop algorithms to compute the spinor norm, and hence to construct a homomorphism from N with kernel the omega group. These algorithms run in lowdegree polynomial time (with a discrete log oracle in some cases) and are implemented in Magma. We also present similar algorithms for the normalisers of the other quasisimple classical groups. This paper is available as a pdf (244kB) file.
