
Journal of Lie Theory 27 (2017), No. 1, 251270 Copyright Heldermann Verlag 2017 SchurWeyl Duality for Special Orthogonal Groups Shripad M. Garge Dept. of Mathematics, Indian Inst. of Technology, Powai  Mumbai 400 076, India shripad@math.iitb.ac.in Anuradha Nebhani Dept. of Mathematics, Indian Inst. of Technology, Powai  Mumbai 400 076, India anuradha.nebhani@gmail.com [Abstractpdf] \def\C{\mathbb{C}} Classical SchurWeyl duality is between the group algebras of the general linear group, GL$_m(\C)$, and the symmetric group, $S_r$; both acting on the $r$th tensor power of the space $\C^m$. To get an analogue of this duality for orthogonal groups, Brauer described the socalled Brauer algebra which surjects onto the commutant of the group algebra of the orthogonal group. He also proved a SchurWeyl duality for orthogonal groups over $\C$ which was later extended by Doty and Hu to all 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. Keywords: SchurWeyl duality, Brauer algebra, orthogonal groups. MSC: 20G05 [ Fulltextpdf (344 KB)] for subscribers only. 