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Lie Groups and Representation Theory
Seminar information archive ～05/01｜Next seminar｜Future seminars 05/02～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2025/05/13
15:45-16:45 Room #128 (Graduate School of Math. Sci. Bldg.)
Mamoru UEDA (The University of Tokyo)
Affine Yangians and non-rectangular W-algebras of type A (Japanese)
Mamoru UEDA (The University of Tokyo)
Affine Yangians and non-rectangular W-algebras of type A (Japanese)
[ Abstract ]
The Yangian is a quantum group introduced by Drinfeld and is a deformation of the current Lie algebra in finite setting. Yangians are actively used for studies of one kind of vertex algebra called a W-algebra. One of the representative results is that Brundan and Kleshchev wrote down a finite W-algebra of type A as a quotient algebra of the shifted Yangian. The shifted Yangian contains a finite Yangian of type A as a subalgebra. De Sole, Kac, and Valeri constructed a homomorphism from this subalgebra to the finite W-algebra of type A by using the Lax operator.
In this talk, I will explain how to construct a homomorphism from the affine Yangian of type A to a non-rectangular W-algebra of type A, which can be regarded as an affine version of the result of De Sole-Kac-Valeri. This homomorphism is expected to lead to a generalization of the AGT conjecture.
The Yangian is a quantum group introduced by Drinfeld and is a deformation of the current Lie algebra in finite setting. Yangians are actively used for studies of one kind of vertex algebra called a W-algebra. One of the representative results is that Brundan and Kleshchev wrote down a finite W-algebra of type A as a quotient algebra of the shifted Yangian. The shifted Yangian contains a finite Yangian of type A as a subalgebra. De Sole, Kac, and Valeri constructed a homomorphism from this subalgebra to the finite W-algebra of type A by using the Lax operator.
In this talk, I will explain how to construct a homomorphism from the affine Yangian of type A to a non-rectangular W-algebra of type A, which can be regarded as an affine version of the result of De Sole-Kac-Valeri. This homomorphism is expected to lead to a generalization of the AGT conjecture.
