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We consider the space
of alternating senary 3-tensors, equipped with the natural action of the group
of invertible linear transformations of
. We describe explicitly the category of
-modules as the category of representations of a quiver with relations, which has finite representation type. We give a construction of the six simple equivariant
-modules and give formulas for the characters of their underlying
-structures. We describe the (iterated) local cohomology groups with supports given by orbit closures, determining, in particular, the Lyubeznik numbers associated to the orbit closures.
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