THE STRUCTURE OF THE YOUNG SYMMETRIZERS FOR SPIN REPRESENTATIONS OF THE SYMMETRICAL GROUP, I

This paper is the first in a series of three papers on the Young symme trizers for the spin representations of the symmetric group. In this o pening paper, it is shown that the projective analogue of the Young sy mmetrizer recently introduced by Nazarov has a structure resembling th e p(lambda)q(lambda)-form exhibited by the classical symmetrizer. In c ontrast to the classical case, our decomposition of the projective sym metrizer requires an additional intermediate factor x(lambda),. This f actor will be studied in greater detail in the later papers, (C) 1998 Academic Press.