Coproduct for affine Yangians and parabolic induction for rectangular $W$-algebras
Representation Theory
2022-01-26 v1 Quantum Algebra
Abstract
We construct algebra homomorphisms from affine Yangians to the current algebras of rectangular -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 -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.
Cite
@article{arxiv.2107.00780,
title = {Coproduct for affine Yangians and parabolic induction for rectangular $W$-algebras},
author = {Ryosuke Kodera and Mamoru Ueda},
journal= {arXiv preprint arXiv:2107.00780},
year = {2022}
}
Comments
35 pages