Affine Super Yangians and Rectangular $W$-superalgebras

Mamoru Ueda

Affine Super Yangians and Rectangular $W$-superalgebras

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arxiv 2002.03479 v4 pith:NNPLGHNT submitted 2020-02-10 math.RT

Mamoru Ueda This is my paper · ORCID

classification math.RT

keywords affinehomomorphismmathfrakrectangularsuperalgebraconstructdense

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abstract

In this paper, we construct a homomorphism from the affine super Yangian $Y_{\ve_1,\ve_2}(\widehat{\mathfrak{sl}}(m|n))$ to the universal enveloping algebra of the rectangular $W$-superalgebra $W^{k}(\mathfrak{gl}(ml|nl),(l^{(m|n)}))$. We also show that the image of this homomorphism is dense provided that $k+(m-n)(l-1)\neq0$.

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