从Frobenius特征标公式到顶点算子  

From Frobenius character formula to vertex operators

作　　者：景乃桓 Naihuan Jing

机构地区：[1]Department of Mathematics,North Carolina State University,Raleigh 27695,USA [2]上海大学理学院数学系,上海200444

出　　处：《中国科学：数学》2018年第11期1717-1728,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11531004)资助项目

摘　　要：本文利用群表示论方法简洁证明了Frobenius对称群特征标公式和Specht圈群特征标公式. Frobenius关于对称群的特征标公式已经显现了顶点算子的雏形,本文提出的证明关键是利用对称群Grothendieck环的乘法公式得到Bernstein顶点算子.同时,本文将此方法推广到圈群链的Grothendieck环,利用顶点算子和广义Clifford代数导出圈群的不可约特征标,简单地证明了Specht关于圈群的特征标公式.In this paper, simplified derivation of Frobenius＇ character formula for the symmetric group and Specht＇s character formula for the wreath products is given. It is shown that vertex operators had their presence in Frobenius formula via the multiplication of the Grothendieck ring. The same method is applied to the Grothendieck ring of the wreath products of symmetric groups and any finite group to give a simplified proof of the Specht formula.

关 键 词：Frobenius特征标公式 顶点算子 Grothendieck环 Specht特征标公式 

分 类 号：O152[理学—数学]