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arXiv · 2107.00780

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

Ryosuke Kodera·Mamoru Ueda
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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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BibTeXRIS

Ryosuke Kodera, Mamoru Ueda. 2021-07-02. Coproduct for affine Yangians and parabolic induction for rectangular $W$-algebras. https://doi.org/10.1007/s11005-021-01500-3

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