报告题目：On the semisimple representation theory of cyclotomic Sergeev algebra
报告人：施磊（中科院数学与系统科学研究院）
报告时间：10月17-18日 13:30-15:30；10月20-22日 13:30-15:30
报告地点：理学院1-102
报告摘要：In this lecture, we will begin by reviewing some fundamentals of superalgebra. This will include key concepts such as supermodules, homomorphisms, Schur’s Lemma, Wedderburn’s Theorem as a superalgebra analogue. We will incorporate many examples throughout this discussion. Next, we will focus on the main topic of the lecture—the cyclotomic Sergeev algebra. This algebra serves as a degenerate and super analogue of the conventional cyclotomic Hecke algebra. We will cover its background, definition, and basic properties. Additionally, we will touch upon categorification theory and its Z-graded lift. We shall focus on semisimple representation theory in this lecture. To this end, we will introduce some related combinatorial concepts and discuss the important separate condition, which parallels the multi-partitions and Poincaré polynomial for the cyclotomic Hecke algebra. We will then delve into the construction of simple modules, including the basis and the actions of standard generators on these modules. Finally, we will explain in detail the construction of primitive idempotents and seminormal bases, along with their applications.
报告人简介：施磊，中科院数学与系统科学研究院博士后。主要研究方向为代数李理论及表示论，在量子群、Hecke代数、Hecke-Clifford代数、箭图Hecke（超）代数等方面取得一系列成果。相关成果发表在Math. Z., Commun. Contemp. Math., J. Algebra, J. Pure Appl. Algebra, Lett. Math. Phys.等国际著名数学学术期刊上。
