Title: Counting the numbers of representations and Kac conjecture

报告人：美国Kansas州立大学数学系林宗柱教授

报告地点：闵行数学楼102报告厅

时间：2012年6月4号下午 3:30~4:30

摘要: With Gabriel's work showing that, for a Dynkin quiver, the indecomposable representations are in one to one correspondence to positive roots of the corresponding Lie algebras, Kac investigated further connections of representations of arbitrary quivers (without loops) to root systems of Kac-Moody Lie algebras and conjectured that for each positive root, the number of absolutely indecomposable representations of the quiver corresponding to this positive rootover a finite field with $q$ elementsis a polynomial of $q$ with nonnegative integer coefficients and the constant term is exactly the dimension of the root space of the Kac-Moody Lie algebra. In this talk I will outline the idea of the proof of conjecture by Huasel et al and discuss some speculations of the conjecture in the non-simply laced cases.