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تسجيل مستخدم جديدThe Green polynomials via vertex operators
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An iterative formula for the Green polynomial is given using the vertex operator realization of the Hall-Littlewood functions. Based on this, (1) a general combinatorial formula of the Green polynomial is given; (2) several compact formulas are given for Greens 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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