Speaker: Professor Weizhong Zhao, Capital Normal University

Inviter: Professor Xingbiao Hu

Title: W-representations of matrix models

Language: Chinese

Time & Venue: 2024.10.30 10:30-11:30 南楼N219

Abstract: W-representations of matrix models give the dual expressions for the partition functions through differentiation rather than integration. More precisely, the partition functions are realized by acting on elementary functions with exponents of the given W-operators. We construct the (β-deformed) partition function hierarchies with W-representations. Some well known superintegrable matrix models are contained in our hierarchies. Moreover we construct the generalized β and (q,t)-deformed partition functions through W representations, where the expansions are respectively with respect to the generalized Jack and Macdonald polynomials labeled by N-tuple of Young diagrams. We find that there are the profound interrelations between our deformed partition functions and the Nekrasov partition functions.