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arXiv · 2508.10271

On the Structure of Multilinear Invariants of a Finite Unitary Reflection Group

A. K. M. Selim Reza·Manabu Oura·Masashi Kosuda
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Abstract

We study the space of multilinear invariants \( V_f \) of degree \( f \) for a specified finite unitary reflection group. A subspace \( W_f \) of typical invariants is also introduced. We note that the dimension of \( W_f \) is given by Catalan number. We explore both spaces for \( f \leq 5 \), 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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A. K. M. Selim Reza, Manabu Oura, Masashi Kosuda. 2025-08-14. On the Structure of Multilinear Invariants of a Finite Unitary Reflection Group. https://arxiv.org/abs/2508.10271

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