2024/02/02 by Ueda, Mamoru
#17B37 #17B69 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2402.01870
In the previous paper, we constructed a homomorphism from the affine Yangian associated with \widehat\mathfraksl(n) to the standard degreewise completion of the affine Yangian associated with \widehat\mathfraksl(n+1). In this article, by using this homomorphism, we construct homomorphisms from the affine Yangian to the universal enveloping algebra of a non-rectangular W-algebra of type A, which are different from the one in \citeU7. Based on this result, we discuss a new definition of the affine shifted Yangian, from which it is expected that there exists a homomorphism to the universal enveloping algebra of a non-rectangular W-algebra of type A. In the appendix, we also show that this homomorphism is related to the one from the quantum affine algebra associated with \widehat\mathfraksl(n) to the quantum affine algebra associated with \widehat\mathfraksl(n+1) given by Li.