q-Immanants and Higher quantum Capelli identites

发布时间：2025-05-12 作者：浏览次数：

Speaker:	景乃桓	DateTime:	2025年5月12日（周一）下午16:00-17:00
Brief Introduction to Speaker: 景乃桓，北卡州立大学		Place:	国交2号楼201
Abstract: I will discuss some recent joint work with Ming Liu and Alex Molev on higher quantum Capelli identities and q-immanants. We construct polynomials parameterized by Young diagrams, whose coefficients are central elements of the quantized enveloping algebra of the general linear algebra. They are shown to provide the higher quantum Capelli identities. These $q$-immanants generalize Drinfeld-Reshetikhin's construction of central elements in Z(U_q(g)) as well as q-analogues of Okounkov's quantum immanants for U(gl(n)). The Harish-Chandra image of the these central elements are certain factorial Schur polynomials.