Yehao Zhou (IPMU) “Type A deformed double current algebras, affine Yangians, rectangular W-algebras, and their coproducts “

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Abstract: In this talk I will start with introducing a new presentation of deformed double current algebra of type gl_k, denoted by A^{(k)}, which is motivated from the study of M2 branes in the twisted M-theory. Then I will explain how to find an algebra embedding from A^{(k)} to the mode algebra of W^{(k)}_\infty, which is a matrix-extended generalization of W_{1+\infty} algebra. The embedding is motivated from the M2 ending on M5 configuration. A^{(k)} can be “doubled” to get an algebra Y^{(k)}. When k is not equal to 2, we can show that Y^{(k)} is isomorphic to affine Yangian of type A_{k-1}. Conjecturally, such isomorphism also holds for k=2. I will also discuss various coproducts of these algebras along the way, which are motivated from the fusions of branes. This talk is based on the joint work with Davide Gaiotto and Miroslav Rapcak (arXiv: 2309.16929).