• Corpus ID: 119684472

# Olshanski's Centralizer Construction and Deligne Tensor Categories

@article{Utiralova2019OlshanskisCC,
title={Olshanski's Centralizer Construction and Deligne Tensor Categories},
author={Alexandra Utiralova},
journal={arXiv: Representation Theory},
year={2019}
}
The family of Deligne tensor categories $\mathrm{Rep}(GL_t)$ is obtained from the categories $\mathbf{Rep}~GL(n)$ of finite dimensional representations of groups $GL(n)$ by interpolating the integer parameter $n$ to complex values. Therefore, it is a valuable tool for generalizing classical statements of representation theory. In this work we introduce and prove the generalization of Olshanski's centralizer construction of the Yangian $Y(\mathfrak{gl}_n)$. Namely, we prove that for generic $t… ## References SHOWING 1-8 OF 8 REFERENCES Centralizer construction for twisted Yangians • Mathematics • 1997 Abstract. For each of the classical Lie algebras$ {\frak g}(n)={\frak o}(2n+1)$,$ {\frak {sp}(2n),{\frak o}(2n)} $of type B, C, D we consider the centralizer of the subalgebra$ {\frak o}(2n-2m)
REPRESENTATION THEORY IN COMPLEX RANK, I
P. Deligne defined interpolations of the tensor category of representations of the symmetric group Sn to complex values of n. Namely, he defined tensor categories Rep(St) for any complex t. This
DELIGNE’S CATEGORY Rep(GLδ) AND REPRESENTATIONS OF GENERAL LINEAR SUPERGROUPS
We classify indecomposable summands of mixed tensor powers of the natural representation for the general linear supergroup up to isomorphism. We also give a formula for the characters of these
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Categories tensorielles
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La Categorie des Representations du Groupe Symetrique St
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