The Genus Expanded Cut-and-join Operator Algebra and Hurwitz Number
主 题: The Genus Expanded Cut-and-join Operator Algebra and Hurwitz Number
报告人: Quan Zheng （SCU）
时 间: 2016-10-12 15:15 - 2016-10-12 17:15
地 点: Room 9, Quan Zhai, BICMR
Abstract. To distinguish the contributions to the generalized Hurwitz number? of the source Riemann surface with different genus, by observing carefully the symplectic surgery and the gluing formulas of the relative GW-invariants, we define the genus expanded? cut-and-join operators, which can form? a differential operator algebra. Moreover, the differential operator algebra? is isomorphic to the central subalgebra of the symmetric group algebra for the finite case,? and is isomorphic is isomorphic to the central subalgebra? of infinite
symmetric group algebra? for the shifted case.? As an application, we get some? differential equations for the generating functions of the Hurwitz numbers? for the source Riemann surface with different genus, thus we can express the generating functions in? terms of the genus expanded? cut-and-join operators.