Title: Generalized Capelli identities

Speaker: Naihuan Jing (North Carolina State Univ)

Time: Monday, June 10, 2024, AM: 10:30-11:30

Venue: Room 3A01, Building No. 37, Wushan Campus

Abstract: The Capelli identity is one of the most important results of classical invariant theory. 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. This is joint work with Jian Zhang.