曹锡华代数论坛（校级学术报告）
题目： Character formulas for Lie superalgebra $gl(m/n)$
报告人：苏育才教授（中科大数学学院）
时间：12月31日（周六）下午4：00--5：00
地点：理科大楼A1510
摘要： In this talk, we present the computation of the generalized Kazhdan- Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebras. Using the result we establish a one to one correspondence between the set of composition factors of an arbitrary $r$-fold atypical $gl_{m|n}$-Kac-module and the set of composition factors of some $r$-fold atypical $gl_{r|r}$-Kac-module. The result of Kazhdan-Lusztig polynomials is also applied to prove a conjectural character formula put forward by van der Jeugt et al in the late 80s. We simplify this character formula to cast it into the Kac-Weyl form, and derive from it a closed formula for the dimension of any finite dimensional irreducible representation of the general linear superalgebra.
