We expect to obtain a realization of finite W-superalgebra of the queer Lie superalgebras by the corresponding Yangian, generalizing a new result in type A Lie superalgebra obtained in our last project. Such a realization is obtained though the study of the type A super Yangian, and we will modify our method so that we may apply similar approaches to the type Q super Yangian and establish a realization for the finite W-superalgebra associated to an arbitrary nilpotent element in a queer Lie superalgebra.We will further study the structure of type A finite W-superalgebra and its representation theory via such a realization. Finally, we would like to study the relationship between the type A super Yangian and the degenerate affine Hecke algebras, such as an analogue of the Arakawa-Suzuki functor. We will also study parallel phenomenons between the type Q super Yangian and the degenerate affine Hecke-Clifford algebras.
|Effective start/end date||1/08/21 → 31/07/22|
- Super Yangian
- Lie superalgebras
- finite W-superalgebras.
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