Untitled

Duke, William

doi:10.1155/s1073792893000121

Cited by 23 publications

(2 citation statements)

References 5 publications

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“…Then we have only to apply linear algebra. The matrix A is diagonalizable and we get 1 4,4,4, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) 1 The matrices X, A, and P can be found at [12].…”

Section: We Shall Consider the Matrixmentioning

confidence: 99%

“…As to this direction in higher genus, see [9,14]. There exist some results based on the fact that the weight enumerator of a self-dual and doubly even binary code is invariant under the action of H g [3,4,13,15]. The correspondence existing among the invariant theory of the finite groups, the theory of modular forms, and combinatorics such as coding theory motivates the notion and study of E-polynomials.…”

Section: Introductionmentioning

confidence: 99%

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Note on the permutation group associated to E-polynomials

IMAMURA¹,

Kosuda²,

OURA³

2022

Journal of Algebra Combinatorics Discrete Structures and Applications

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“…Then we have only to apply linear algebra. The matrix A is diagonalizable and we get 1 4,4,4, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) 1 The matrices X, A, and P can be found at [12].…”

Section: We Shall Consider the Matrixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Note on the permutation group associated to E-polynomials

IMAMURA¹,

Kosuda²,

OURA³

2022

Journal of Algebra Combinatorics Discrete Structures and Applications

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On the Ring of Simultaneous Invariants for the Gleason–MacWilliams Group

Bannaĭ

Ozeki

Teranishi

1999

European Journal of Combinatorics

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We construct a canonical generating set for the polynomial invariants of the simultaneous diagonal action (of arbitrary number of l factors) of the two-dimensional finite unitary reflection group G of order 192, which is called the group No. 9 in the list of Shephard and Todd, and is also called the Gleason-MacWilliams group. We find this canonical set in the vector space (⊗ l i=1 V ) G , where V denotes the (dual of the) two-dimensional vector space on which the group G acts, by applying the techniques of Weyl (i.e., the polarization process of invariant theory) to the invariants C[x, y] G 0 of the two-dimensional group G 0 of order 48 which is the intersection of G and S L(2, C). It is shown that each element in this canonical set corresponds to an irreducible representation which appears in the decomposition of the action of the symmetric group S l . That is, by letting the symmetric group S l acts on each element of the canonical generating set, we get an irreducible subspace on which the symmetric group S l acts irreducibly, and all these irreducible subspaces give the decomposition of the whole space (⊗ l i=1 V ) G . This also makes it possible to find the generating set of the simultaneous diagonal action (of arbitrary l factors) of the group G. This canonical generating set is different from the homogeneous system of parameters of the simultaneous diagonal action of the group G. We can construct Jacobi forms (in the sense of Eichler and Zagier) in various ways from the invariants of the simultaneous diagonal action of the group G, and our canonical generating set is very fit and convenient for the purpose of the construction of Jacobi forms.

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The General Noncompact Symmetric Space

Terras

2016

Harmonic Analysis on Symmetric Spaces—Higher Rank Spaces, Positive Definite Matrix Space and Generalizations

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Cited by 23 publications

References 5 publications

Note on the permutation group associated to E-polynomials

Note on the permutation group associated to E-polynomials

On the Ring of Simultaneous Invariants for the Gleason–MacWilliams Group

The General Noncompact Symmetric Space

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