On the Structure of Multilinear Invariants of a Finite Unitary Reflection Group
Abstract
We study the space of multilinear invariants \( Vf \) of degree \( f \) for a specified finite unitary reflection group. A subspace \( Wf \) of typical invariants is also introduced. We note that the dimension of \( Wf \) is given by Catalan number. We explore both spaces for \( f ≤ 5 \), noting that their dimensions differ based on the value of \( f \). We explicitly determine the bases for both spaces, and then we establish the relationship between the vectors of the two bases.
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