Affine Yangians and some cosets of non-rectangular W-algebras

2024/04/28 by Mamoru Ueda, Ueda, Mamoru
Computer Science · Mathematics · #17B37 #17B69 #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2404.18064

openalex publication_date 2024/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a homomorphism from the affine Yangian associated with \widehat\mathfraksl(q_u-q_u+1) to the universal enveloping algebra of a W-algebra associated with \mathfrakgl(∑_s=1^lq_s) and a nilpotent element of type (1^q₁-q₂,2^q₂-q₃,…,(l-1)^q_l-1-q_l,l^q_l) by using the coproduct and evaluation map for the affine Yangian and the Miura map for non-rectangular W-algebras. As an application, we give a homomorphism from the affine Yangian to some cosets of non-rectangular W-algebras.

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