报告人：陈志玮 副教授

工作单位：台湾中央大学

报告时间：2023年10月31日，11月7日,14日，21日，28日13:50-14:50&20:00-21:00

参会方式：腾讯会议ID：849 9770 2887

报告简介：

(A). Background:

Whittaker modules over finite-dimensional complex semisimple Lie algebras are a natural generalization of modules in the BGG category O. A classification of simple Whittaker modules was obtained by McDowell and Milicic-Soergel based on the seminal work of Kostant. This construction was obtained by means of certain standard Whittaker modules. Furthermore, Milicic and Soergel developed the categoryN that contains these structural Whittaker modules. It contains a thick version of the BGG category O as a direct summand. Our goal is to introduce these classical results and to report on some recent progress of Whittaker modules in the category N for Lie superalgebras.

(B). Goals (expected):

Talk 1. In the first talk, we will review some background materials on the BGG category O for semisimple Lie algebras.

Talk 2. We will introduce the classical results of Kostant [1], McDowell [2], Milicic -Soergel [3] and Backelin [4]. We will study the standard Whittaker modules and and their composition factors.

Talk 3. We introduce the Whittaker category N. Furthermore, we will study the structure of the category N.

Talks 4, 5. Finally, we explain the construction of standard and simple Whittaker modules for Lie superalgebras. Furthermore, we explain an equivalence between a full subcategory of N and a certain projectively presentable modules in the category O.

(C). References:

[1]. B. Kostant. On Whittaker vectors and representation theory. Inv. Math. 48.2 (1978): 101-184.

[2]. E. McDowell, On modules induced from Whittaker modules. J. Algebra 96 (1985), 161–177.

[3]. D. Milicic and W. Soergel. The composition series of modules induced from Whittaker modules. Comment. Math. Helv. 72.(1997), no.4, 503-520.

[4]. E. Backelin. Representation of the category O in Whittaker categories. Int. Math. Res. Notices 4 (1997), 153–172.

[5]. C.-W. Chen. Whittaker modules for classical Lie superalgebras. Comm. Math. Phy. 388 (2021), 351–383.

[6]. C.-W. Chen., S.-J. Cheng and V. Mazorchuk. Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras. Comm. Math. Phy., 401, pages 717–768 (2023).

报告人简介：陈志玮，中国台湾中央大学数学与统计学院副教授，于2016年毕业于台湾大学，主要从事与李理论的表示范畴相关的研究。至今为止在Comm. Math. Phys., Trans. Amer. Math. Soc. J. Lond. Math. Soc.,Int. Math. Res. Not., Math. Z.等杂志发表高水平论文20多篇。