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

The Fundamental Theorem ofq-clan geometry implies (among other things) that all automorphisms of the generalized quadrangle GQ(image) of order (q2, q) associated with a q-clan image which fix a special pair of points are automorphisms of the elation group of the quadrangle. When q = 2e, 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(image). 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.