An Example of Homomorphisms from the Guay's affine Yangians to non-rectangular $W$-algebras

Mamoru Ueda

An Example of Homomorphisms from the Guay's affine Yangians to non-rectangular $W$-algebras

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arxiv 2211.14968 v3 pith:BFMIDE7U submitted 2022-11-27 math.QA math.RT

Mamoru Ueda This is my paper · ORCID

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abstract

We construct a non-trivial homomorphism from the Guay's affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$ to the universal enveloping algebra of the $W$-algebra associated with a Lie algebra $\mathfrak{gl}(m+n)$ and its nilpotent element whose Jordan block of type $(2^{n},1^{m-n})$ for $m>n$.

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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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