The Garnir Relations for Weyl Groups of Type $C_n$

Himmet Can

Abstract


The Garnir relations play a very important role in giving combinatorial constructions of representations of the symmetric groups. For the Weyl groups of type $C_n$, having obtained the alternacy relation, we give an explicit combinatorial description of the Garnir relation associated with a $\Delta$-tableau in terms of root systems. We then use these relations to find a $K$-basis for the Specht modules of the Weyl groups of type $C_n$.


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