报告人：Chih-Whi Chen

Department of Mathematics, Uppsala University

题目：Representation theory of the periplectic Lie superalgebra

时间：2018年4月27日15:15

地点：海韵行政楼B313

摘要：Lie superalgebras are generalizations of Lie algebras and are an importanttool for physicists in the study of supersymmetry. In particular, their representationtheory, have recently enjoyed a surge of considerable interest. In his celebrated paper[K2], a Killing-Cartan type classification of finite-dimensional complex simple Lie supealgebras was established by Kac. The most important subclass of the simple Lie super-algebras is called basic classical and it includes the series of type A. Besides, he found two families of exotic classical simple Lie superalgebras, which are called strange Liesuperalgebras consisting of periplectic Lie superalgebras and queer Lie superalgebras.

The periplectic Lie superalgebra p(n) is a superanalogue of the orthogonal or symplectic Lie algebra preserving an odd non-degenerate symmetric or skew-symmetricbilinear form. While the BGG categories O for the other finite-dimensional simple Liesuperalgebras are not well understood at present, the irreducible characters and linkageprinciples for most of them have been worked out with the exception of p(n).

This talk will start with the introduction about myself, including my ducation,research interest and results. In this talk, I will present my recent research on linkageprinciple and the approach to irreducible characters for the BGG category O.

References:

[K2] V. Kac, Representations of classical Lie superalgebras. Differential geometrical methods inmathematical physics, II (Proc. Conf., Univ. Bonn, Bonn, 1977), pp. 597{626, Lecture Notes

in Math. 676, Springer, Berlin, 1978.

联系人:郭淑敏老师

欢迎广大师生参加!