\def\C{\mathbb{C}} 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 $r$th 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 onto 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 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.
1
Dept. of Mathematics, Indian Inst. of Technology, Powai -- Mumbai 400 076, India
Shripad M. Garge; Anuradha Nebhani. Schur-Weyl Duality for Special Orthogonal Groups. Journal of Lie Theory, Tome 27 (2017) no. 1, pp. 251-270. http://geodesic.mathdoc.fr/item/JOLT_2017_27_1_a13/
@article{JOLT_2017_27_1_a13,
author = {Shripad M. Garge and Anuradha Nebhani},
title = {Schur-Weyl {Duality} for {Special} {Orthogonal} {Groups}},
journal = {Journal of Lie Theory},
pages = {251--270},
year = {2017},
volume = {27},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2017_27_1_a13/}
}
TY - JOUR
AU - Shripad M. Garge
AU - Anuradha Nebhani
TI - Schur-Weyl Duality for Special Orthogonal Groups
JO - Journal of Lie Theory
PY - 2017
SP - 251
EP - 270
VL - 27
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2017_27_1_a13/
ID - JOLT_2017_27_1_a13
ER -
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%J Journal of Lie Theory
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%P 251-270
%V 27
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2017_27_1_a13/
%F JOLT_2017_27_1_a13
