Schur Q-Polynomials and Kontsevich-Witten Tau Function  

作　　者：Xiaobo Liu Chenglang Yang 

机构地区：[1]School of Mathematical Sciences and Beijing International Center for Mathematical Research,Peking University,Beijing,China

出　　处：《Peking Mathematical Journal》2024年第2期713-758,共46页北京数学杂志（英文）

基　　金：partially supported by NSFC grants 11890662 and 11890660.

摘　　要：Using matrix model,Mironov and Morozov recently gave a formula which represents Kontsevich-Witten tau function as a linear expansion of Schur Q-polynomials.In this paper,we will show directly that the Q-polynomial expansion in this formula satisfies the Virasoro constraints,and consequently obtains a proof of this formula without using matrix model.We also give a proof for Alexandrov’s conjecture that Kontsevich-Witten tau function is a hypergeometric tau function of theBKPhierarchy after re-scaling.

关 键 词：Kontsevich-Wittentaufunction Schur Q-polynomials BKP hierarchy 

分 类 号：O15[理学—数学]