報告題目：On the semisimple representation theory of cyclotomic Sergeev algebra

　　報告人：施磊（中科院數學與系統科學研究院）

　　報告時間：10月17-18日 13:30-15:30；10月20-22日 13:30-15:30

　　報告地點：理學院1-102

　　報告摘要：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.

　　報告人簡介：施磊，中科院數學與系統科學研究院博士后。主要研究方向為代數李理論及表示論，在量子群、Hecke代數、Hecke-Clifford代數、箭圖Hecke（超）代數等方面取得一系列成果。相關成果發表在Math. Z., Commun. Contemp. Math., J. Algebra, J. Pure Appl. Algebra, Lett. Math. Phys.等國際著名數學學術期刊上。