arXiv 2104.044112021-04math.QAmath.COmath.RT

The Green polynomials via vertex operators

Naihuan Jing, Ning Liu

备注：: 19 pages; updated version
发表信息：: J. Pure Appl. Algebra 226 (2022), 107032, 17pp
DOI：: 10.1016/j.jpaa.2022.107032

英文摘要：

An iterative formula for the Green polynomial is given using the vertex operator realization of the Hall-Littlewood function. Based on this, (1) a general combinatorial formula of the Green polynomial is given; (2) several compact formulas are given for Green's polynomials associated with upper partitions of length $\leq 3$ and the diagonal lengths $\leq 3$; (3) a Murnaghan-Nakayama type formula for the Green polynomial is obtained; and (4) an iterative formula is derived for the bitrace of the finite general linear group $G$ and the Iwahori-Hecke algebra of type $A$ on the permutation module of $G$ by its Borel subgroup.

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