Title: Generalized Capelli Identities
Speaker: Naihuan Jing
Affiliation: North Carolina State University, USA
Time: June 26, 2025, 10:30-12:30
Location: Seminar Room 5, Mathematics Building, Jilin University
Abstract:
The Capelli identity stands as one of the cornerstone results in classical invariant theory. This talk explores Capelli identities from multiple perspectives. We will introduce a novel generalization of the Capelli identity for immanants, extending Okounkov's earlier work. Additionally, we present generalized Turnbull's identities applicable to both symmetric and antisymmetric matrices, along with the generalized Howe-Umeda-Kostant-Sahi identities for antisymmetric matrices - the latter confirming a conjecture by Caracciolo, Sokal, and Sportiello. This represents joint work with Jian Zhang.
Speaker's Biography:
Naihuan Jing, Professor Emeritus at North Carolina State University, earned his Ph.D. from Yale University. His research encompasses infinite-dimensional Lie algebras, quantum groups, representation theory, algebraic combinatorics, and quantum computing. Prof. Jing's seminal contributions to symmetric function theory include operators that bear his name ("Jing operators"). He has published nearly 100 papers in leading mathematical journals and edited five scholarly volumes. His work continues to influence multiple areas of modern algebra and mathematical physics.
