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2022•Journal of Mathematical PhysicsOpen access

Affine super Yangians and rectangular W -superalgebras

Mamoru Ueda

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Abstract

Motivated by the Alday-Gaiotto-Tachikawa (AGT) conjecture, we construct a homomorphism from the affine super Yangian Yε1,ε2(sl̂(m|n)) to the universal enveloping algebra of the rectangular W-superalgebra Wk(gl(ml|nl),(l(m|n))) for all m ≠ n, m, n ≥ 2 or m ≥ 3, n = 0. Furthermore, we show that the image of this homomorphism is dense, provided that k + (m − n)(l − 1) ≠ 0.

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Motivated by the Alday-Gaiotto-Tachikawa (AGT) conjecture, we construct a homomorphism from the affine super Yangian Yε1,ε2(sl̂(m|n)) to the universal enveloping algebra of the rectangular W-superalgebra Wk(gl(ml|nl),(l(m|n))) for all m ≠ n, m, n ≥ 2 or m ≥ 3, n = 0. Furthermore, we show that the image of this homomorphism is dense, provided that k + (m − n)(l − 1) ≠ 0.

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Available abstract

Motivated by the Alday-Gaiotto-Tachikawa (AGT) conjecture, we construct a homomorphism from the affine super Yangian Yε1,ε2(sl̂(m|n)) to the universal enveloping algebra of the rectangular W-superalgebra Wk(gl(ml|nl),(l(m|n))) for all m ≠ n, m, n ≥ 2 or m ≥ 3, n = 0. Furthermore, we show that the image of this homomorphism is dense, provided that k + (m − n)(l − 1) ≠ 0.

Key concepts: Yangian, Homomorphism, Affine transformation, Mathematics, Conjecture, Lie superalgebra, Superalgebra, Pure mathematics

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