Journal of Lie Theory

no. 1
Schur-Weyl Duality for Special Orthogonal Groups
Journal of Lie Theory, Volume 27 (2017) no. 1, pp. 251-270
\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.
DOI: 10.5802/jolt.944
Classification: 20G05
Keywords: Schur-Weyl duality, Brauer algebra, orthogonal groups 
@article{JOLT_2017_27_1_a13,
     author = {S. M. Garge and A. Nebhani},
     title = {Schur-Weyl {Duality} for {Special} {Orthogonal} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {251--270},
     year = {2017},
     volume = {27},
     number = {1},
     doi = {10.5802/jolt.944},
     zbl = {1430.20046},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.944/}
}
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S. M. Garge; A. Nebhani. Schur-Weyl Duality for Special Orthogonal Groups. Journal of Lie Theory, Volume 27 (2017) no. 1, pp. 251-270. doi: 10.5802/jolt.944

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