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Coproduct for affine Yangians and parabolic induction for rectangular $W$-algebras

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arxiv 2107.00780 v1 pith:E5YBDJ4O submitted 2021-07-02 math.RT math.QA

Ryosuke Kodera , Mamoru Ueda This is my paper · ORCID
classification math.RTmath.QA
keywords affinealgebrasyangiansrectangularcoproducthomomorphismsparabolicrepresentations
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abstract

We construct algebra homomorphisms from affine Yangians to the current algebras of rectangular $W$-algebras both in type A. The construction is given via the coproduct and the evaluation map for the affine Yangians. As a consequence, we show that parabolic inductions for representations of the rectangular $W$-algebras can be regarded as tensor product representations of the affine Yangians under the homomorphisms. The same method is applicable also to the super setting.

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Cited by 1 Pith paper

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  1. Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues

    hep-th 2025-01 conditional novelty 7.0 of 10

    For quivers satisfying a no-overlap condition, flavored BPS indices are computed by crystal melting derived from Jeffrey-Kirwan residues, and new double quiver algebras are constructed whose crystal representations en...

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