On the exact sequences of FW6- pair of hooks representation modules over a field of characteristic 0

Abstract

The intention of this paper is to find the exact and split sequences of the sub modules of FW₆-second and third pair of hooks representation modules, when F be a field of characteristic 0 . This intention is revealing by presenting the main results theorems (3-1) and (3-2), where we gave two of this kind of sequences.

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Here we refer that depending on the structural constructing of the elements (modules) of these sequences or it‘s sub modules by counting the dimensions was essential for proving these theorems.