Yangian Gelfand-Zetlin bases in the Dorey-Tong-Turner matrix model Hilbert space

Speaker: Yehao Zhou (IPMU)

Time: 14:00 ~ 15:00, Monday, Aug. 5, 2024



Location: 上海市杨浦区伟成路62号 企业中心3号楼6层 上海数学与交叉学科研究院(SIMIS)会议室

Zoom Meeting No.: 423 317 8953 (Password: SIMIS)

Title: Yangian Gelfand-Zetlin bases in the Dorey-Tong-Turner matrix model Hilbert space

Abstract: Dorey, Tong, and Turner obtained a model of the non-Abelian fractional quantum Hall effect from a matrix model. Their matrix model is a generalization of spin Calogero-Moser model in the sense that internal symmetry acts on higher symmetric representation instead of fundamental representation. In this talk we consider the analog of spin Calogero-Sutherland Hamiltonian in this matrix model, and we will see that the this Hamiltonian is part of quantum determinant of a Yangian algebra acting on the Hilbert space. We will show that the Yangian action on the Hilbert space is semisimple and characterize each simple constituent. Moreover, the action of the Gelfand-Zetlin subalgebra of the Yangian has simple spectrum and the eigenvectors are labelled by certain combinatorial patterns. We compute the eigenvalues of the Gelfand-Zetlin subalgebra action, in particular we obtain the eigenvalues of the Hamiltonian. This generalizes Uglov’s result on Yangian Gelfand-Zetlin bases in the spin Calogero-Sutherland model.