A型有限W-超代數研究方法之推廣與應用;Generalization and Applications of Research Methods of Type a Finite W-Superalgebras

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/84739

Title:	A型有限W-超代數研究方法之推廣與應用;Generalization and Applications of Research Methods of Type a Finite W-Superalgebras
Authors:	彭勇寧
Contributors:	數學系
Keywords:	超楊子;李超代數;有限W超代數;;Super Yangian;Lie superalgebras;finite W-superalgebras.
Date:	2020-12-08
Issue Date:	2020-12-09 10:49:37 (UTC+8)
Publisher:	科技部
Abstract:	本研究計畫預期將前一期計畫結果中得到的A型有限W超代數的某種實現推廣至Q型有限W超代數上。此種實現是透過對A型超楊子的研究而得到的，而我們會將此種方法加以適當的修正將其應用到Q型超楊子的研究上，並且得到Q型有限W超代數（對於任意給定的Q型零冪元素）的實現。此外，我們也會利用上述的實現更加深入研究A型有限W超代數的結構以及其表現理論。我們希望能研究A型超楊子與退化仿射赫克代數(degenerate affine Hecke algebras)之間的關係，例如Arakawa-Suzuki函子的構造與其結果，並同時研究Q型超楊子與退化仿射赫克-克里夫代數(degenerate affine Hecke-Clifford algebras)當中的平行結果。 ;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.
Relation:	財團法人國家實驗研究院科技政策研究與資訊中心
Appears in Collections:	[Department of Mathematics] Research Project

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