Abstract: The Capelli identity is one of the most important results of classical invariant theory. It played a central role in Weyl's famous book "The Classical Groups". In this talk, we will discuss the Capelli identities from different points of view. A new generalization of Capelli identity for immanant will be introduced that generalizes Okounkov's identities. We will also present generalized Turnbull's identities for both symmetric and antisymmetric matrices, as well as the generalized Howe-Umeda-Kostant-Sahi identities for antisymmetric matrices which confirm the conjecture of Caracciolo, Sokal and Sportiello.

报告人简介：景乃桓现为美国北卡州立大学教授。曾获国家杰出青年基金(B)，长江学者讲座教授，德国洪堡研究基金，美国富尔布莱特学者等荣誉。在耶鲁大学获博士学位后，曾在美国普林斯顿高等研究院、密西根大学、堪萨斯大学等任教或从事研究工作。作为客座教授多次访问美国伯克利数学研究所、德国波恩马普数学研究所、德国莱比锡马普应用数学所等数学中心。主要研究方向为表示论，量子群、顶点算子代数、代数组合和量子计算等。