arXiv subjects

Masashi Kosuda

Publications and source records attributed to Masashi Kosuda.

8 recordsLinked to original sources

arXiv2026

Vector-Valued Invariants Associated with All Irreducible Representations for a Finite Group

We investigate the complex reflection group $\mathfrak{G}$ associated with the octahedral group, identified as the ninth entry in the Shephard-Todd classification. We determine all irreducible representations of $\mathfrak{G}$ and compute the character table. Moreover, for each representation, we compute the module of vector-valued invariants and relate it to the fundamental invariants of the octahedral group. Additionally, we derive explicit dimension formulas for the corresponding rings of invariants.

math.RT↗

arXiv2025

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

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.

math.CO↗

arXiv2025

Some calculations of centralizer rings of a complex reflection group

Let H1 be the complex reflection group of order 96. For the tensor products of faithful transitive permutation representations of H1, we determine the structures of the centralizer rings. This complements the work of Imamura-Kosuda-Oura.

math.CO↗

arXiv2025

Computation of Vector-Valued Invariants for a Finite Complex Reflection Group

We consider the complex reflection group $ \mathcal{G} $, identified as No. 8 in the Shephard-Todd classification. In this paper, we present computations of the vector-valued invariants associated with various representations of $ \mathcal{G} $. Additionally, we investigate the structure of the corresponding invariant rings.

math.RA↗

arXiv2017

Centralizer algebras of the group associated to ${\mathbb Z}_4$-codes

The purpose of this paper is to investigate the finite group which appears in the study of the Type II $\mathbf{Z}_4$-codes. To be precise, it is characterized in terms of generators and relations, and we determine the structure of the centralizer algebras of the tensor representations of this group.

math.RT↗

arXiv2015

Centralizer algebras of the primitive unitary reflection group of order $96$

Among the unitary reflection groups, the one on the title is singled out by its importance in, for example, coding theory and number theory. In this paper we start with describing the irreducible representations of this group and then examine the semi-simple structure of the centralizer algebra in the tensor representation.

math.RT↗

arXiv2014

Coxeter elements of the symmetric groups whose powers afford the longest

In this article, we first show that in case $n$ is even which Coxeter element in $\mathfrak{S}_{n}$ affords the longest by taking its power to $n/2$. We also show that in case $n$ is odd which Coxeter element affords the longest in $\mathfrak{S}_{n}$.

math.GR↗

arXiv2010

Partition Algebra, its Characterization and Representations

In this note we give representations for the partition algebra A_3(Q) in Young's seminormal form. For this purpose, we also give characterizations of A_n(Q) and$A_{n-1/2}(Q).

math.RT↗