Speaker：Naihuan Jing (North Carolina State University)

Time：2025-6-8 10:30

Location：Conference Room S102 at Experiment Building at Haiyun Campus

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. This is joint work with Jian Zhang.