A Note on Schur-Weyl Dualities for GL(m) and GL(m|n)

We use a unified elementary approach to prove the second part of classical, mixed, super, and mixed super Schur-Weyl dualities for general linear groups and supergroups over an infinite ground field of arbitrary characteristic. These dualities describe the endomorphism algebras of the tensor space a...

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Bibliographic Details
Published in:Algebras and representation theory 2024-10, Vol.27 (5), p.1957-1979
Main Author: Marko, František
Format: Article
Language:English
Subjects:
Algebra
Associative Rings and Algebras
Commutative Rings and Algebras
Fields (mathematics)
Group theory
Mathematics
Mathematics and Statistics
Non-associative Rings and Algebras
Tensors
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Summary:We use a unified elementary approach to prove the second part of classical, mixed, super, and mixed super Schur-Weyl dualities for general linear groups and supergroups over an infinite ground field of arbitrary characteristic. These dualities describe the endomorphism algebras of the tensor space and mixed tensor space, respectively, over the group algebra of the symmetric group and the Brauer wall algebra, respectively. Our main new results are the second part of the mixed Schur-Weyl dualities and mixed super Schur-Weyl dualities over an infinite ground field of positive characteristic.
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-024-10290-w