数学学科2026系列学术报告之二十七

　　报告题目：Schur Elements for Cyclotomic Hecke-Clifford Superalgebras and Applications

　　报告人：施磊（马克斯普朗克数学研究所）

　　报告时间：7月1号10：00-11：00

　　报告地点：理学院1-301

　　报告摘要：This talk is based on joint work with Shuo Li. I will discuss recent results on Schur elements for cyclotomic Hecke-Clifford superalgebras and their degenerate analogues. After recalling the role of Schur elements in the construction of graded cellular bases for quiver Hecke algebras, following Brundan-Kleshchev, Hu-Mathas, and Evseev-Mathas, I will explain how the cyclotomic Hecke-Clifford setting is related to quiver Hecke-Clifford superalgebras via the Kang-Kashiwara-Tsuchioka isomorphism. I will then describe modified trace forms which produce symmetric or supersymmetric structures, and state explicit Schur element formulas in the split semisimple case.

　　As applications, these formulas yield semisimplicity criteria and provide the trace-denominator control needed in the construction of generalized graded cellular bases for certain cyclotomic quiver Hecke-Clifford superalgebras. This gives a super analogue of the deformation-and-specialization strategy used in the ordinary quiver Hecke setting.

　　报告人简介：施磊，德国马普所博士后。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。