A tensor product action on q-clan generallzed quadrangles with q = 2 e

Abstract

The Fundamental Theorem of q-clan geometry implies (among other things) that all automorphisms of the generalized quadrangle GQ( C ) of order ( q 2, q) associated with a q-clan C which fix a special pair of points are automorphisms of the elation group of the quadrangle. When q = 2 e , with a slight modification of the usual representation, we describe these automorphisms in terms of tensor products of pairs of matrices in GL(2, q). The resulting efficiency in computation allows a simplified description of the automorphisms of GQ( C ). We apply the general theory to give an improve description of the induced stabilizers of the ovals in PG(2, q) that are associated with the new Subiaco q-clans introduced and studied in the recent literature.