In this talk, I first review the role of affine Yangian (AY) to prove AGT conjecture. I emphasize that the duality in the representation plays an essential role to prove the conjecture. I also explain that the connection with the integrability as the name of the algebra suggests. In the second part, if the time permits, I would like to explain my recent work on the corner vertex operator algebra. Some emphasis is put on the connection with the plane partition realization of the minimal models.