Schur-Weyl Duality for Special Orthogonal Groups

摘要

Classical Schur-Weyl duality is between the group algebras of the general linear group, GL(m)(C), and the symmetric group, S-r; both acting on the rth tensor power of the space C-m. To get an analogue of this duality for orthogonal groups, Brauer described the so-called Brauer algebra which surjects on to the commutant of the group algebra of the orthogonal group. He also proved a Schur-Weyl duality for orthogonal groups over C which was later extended by Doty and Hutoall infinite fields of characteristic not two. In this paper, we prove the analogous duality for the special orthogonal groups over any infinite field of characteristic not two.