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

2025/08/14 by Reza, A. K. M. Selim, Oura, Manabu, Kosuda, Masashi
#13A50 #20C30 #20F55 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.10271

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 \( f ≤ 5 \), 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.

Citations

• Invariants of multidimensional time series based on their\n iterated-integral signature
• Centralizer algebras of the primitive unitary reflection group of order 96

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