ON THE SPINOR NORM ON UNITARY GROUPS

Abstract

Let F be a field of odd characteristic, E be a finite extension of F equipped an involution with subfield of fixed points E0 containing F and V be a finite dimensional E-vector space with a non-degenerate hermitian form h. We show a link between the spinor norm in the unitary group U(V,h) and the calculus of determinants and discriminants. Then we show a formula which links the spinor norm in U(V,h) and the spinor norm in the orthogonal group O(V,bh) defined by a non-degenerate symmetric bilinear form bh associated to h.