Modular finite W-algebras and shifted Yangians

发布时间：2021-11-11 作者：浏览次数：

Speaker:	Lewis Topley	DateTime:	2021年11月19日(周五)下午4：30-6：00
Brief Introduction to Speaker: Lewis Topley, 英国巴斯大学, 主要研究兴趣包括：李代数与代数群的模表示、模有限W-代数、素特征域上的 Yangian、 Poisson 代数与形变理论等。		Place:	腾讯会议，会议号请联系常浩老师
Abstract:Let G be a reductive algebraic group over an algebraically closed field of characteristic p > 0. The rep. theory of g=Lie(G) has been studied extensively over the past 70 years. The principal difference between the rep. theory of g and the rep. theory of a complex semisimple Lie algebras results from the p-centre, a large central subalgebra of the enveloping algebra. Kac-Weisfeiler made precise conjectures relating the dimensions of representations to the G-orbits of p-central characters. Whilst refining his proof of the second KW conjecture, Premet introduced a new f. d. algebra which is now known as the restricted finite W-algebra. In recent work with Goodwin, we have worked out some general features of the structure of (unrestricted) finite W-algebras and relate their representation theory to the enveloping algebra. Again, the p-centre plays a central role in the theory. In type A the finite W-algebra can be understood as a truncated shifted Yangian, following work of Brundan an...