17 citations · 44 across the 21 of their papers we have counts for
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Generating Sets for the Kernels of Frobenius Polarization Operators
Naoya Yamaguchi
We study generating sets for the kernels of the Frobenius polarization operators associated with elements of finite groups. By applying the discrete Fourier transform on each coset…
Group Permanents of Abelian -Groups and Young Diagrams
Naoya Yamaguchi, Yuka Yamaguchi
We study the number $\Nu(\Per(G_λ))$ of distinct monomials with nonzero coefficients in the group permanent of an abelian -group associated with a partition of a posit…
Group Determinants and Invariant Rings
Yuka Yamaguchi, Naoya Yamaguchi
In the study of group determinants, Frobenius introduced certain partial differential operators. This paper presents several results concerning the invariant rings derived from the…
First and Second Fundamental Theorems for Invariant Rings Generated by Circulant Determinants
Naoya Yamaguchi, Hiroyuki Ochiai, Yuka Yamaguchi
In this paper, we give the first and second fundamental theorems of invariant theory for certain invariant rings whose generators are expressed by circulant determinants.
Principal Specialization of Monomial Symmetric Polynomials and Group Determinants of Cyclic Groups
Naoya Yamaguchi, Yuka Yamaguchi, Genki Shibukawa
In this paper, we study the principal specialization of monomial symmetric polynomials and investigate the special values of these polynomials at \[ ζ_{(n,k)} := ( 1, ζ_n, ζ_n^2, \…
Generalized Dedekind's theorem and its application to integer group determinants
Naoya Yamaguchi, Yuka Yamaguchi
In this paper, we give a refinement of a generalized Dedekind's theorem. In addition, we show that all possible values of integer group determinants of any group are also possible…
Remark on Laquer's theorem for circulant determinants
Naoya Yamaguchi, Yuka Yamaguchi
Olga Taussky-Todd suggested the problem of determining the possible values of integer circulant determinants. To solve a special case of the problem, Laquer gave a factorization of…
Generalized group determinant gives a necessary and sufficient condition for a subset of a finite group to be a subgroup
Naoya Yamaguchi, Yuka Yamaguchi
We generalize the concept of the group determinant and prove a necessary and sufficient novel condition for a subset to be a subgroup. This development is based on the group determ…
Study-type determinants and their properties
Naoya Yamaguchi
In this paper, we define the concept of the Study-type determinant, and we present some properties of these determinants. These properties lead to some properties of the Study dete…
Factorizations of group determinant in group algebra for any abelian subgroup
Naoya Yamaguchi
We give a further extension and generalization of Dedekind's theorem over those presented by Yamaguchi. In addition, we give two corollaries on irreducible representations of finit…
Capelli elements of the group algebra
Naoya Yamaguchi
Inspired by the Capelli identities for group determinants obtained by Tôru Umeda, we give a basis of the center of the group algebra of any finite group by using Capelli identities…
Generalization of Frobenius' theorem for group determinants
Naoya Yamaguchi
Frobenius built a representation theory of finite groups in the process of obtaining the irreducible factorization of the group determinant. Here, we give a generalization of Frobe…
An extension and a generalization of Dedekind's theorem
Naoya Yamaguchi
For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem.…
Factorization of group determinant in some group algebras
N. Yamaguchi
We give an analog of Frobenius' theorem about the factorization of the group determinant on the group algebra of finite abelian groups and we extend it into dihedral groups and gen…