Converting immanants on singular symmetric matrices

M. A. Duffner; A. E. Guterman

doi:10.1134/s1995080217040060

Converting immanants on singular symmetric matrices

M. A. Duffner, A. E. Guterman

Research output: Contribution to journal › Article › peer-review

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Abstract

Let Σ_n(F) denote the space of all n×n symmetricmatrices over the complex field F, and χ be an irreducible character of S_n and d_χ the immanant associated with χ. The main objective of this paper is to prove that the maps Φ: Σ_n(F) → Σ_n(F) satisfying d_χ(Φ(A) + αΦ(B)) = det(A + αB) for all singular matrices A, B ∈ Σ_n(F) and all scalars α ∈ F are linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on the set of all symmetric matrices.

Original language	English
Pages (from-to)	630-636
Number of pages	7
Journal	Lobachevskii Journal of Mathematics
Volume	38
Issue number	4
DOIs	https://doi.org/10.1134/s1995080217040060
State	Published - 1 Jul 2017
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2017, Pleiades Publishing, Ltd.

Keywords

Determinant
converters
permanent
symmetric matrices

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10.1134/s1995080217040060

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abstract = "Let Σn(F) denote the space of all n×n symmetricmatrices over the complex field F, and χ be an irreducible character of Sn and dχ the immanant associated with χ. The main objective of this paper is to prove that the maps Φ: Σn(F) → Σn(F) satisfying dχ(Φ(A) + αΦ(B)) = det(A + αB) for all singular matrices A, B ∈ Σn(F) and all scalars α ∈ F are linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on the set of all symmetric matrices.",

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N2 - Let Σn(F) denote the space of all n×n symmetricmatrices over the complex field F, and χ be an irreducible character of Sn and dχ the immanant associated with χ. The main objective of this paper is to prove that the maps Φ: Σn(F) → Σn(F) satisfying dχ(Φ(A) + αΦ(B)) = det(A + αB) for all singular matrices A, B ∈ Σn(F) and all scalars α ∈ F are linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on the set of all symmetric matrices.

AB - Let Σn(F) denote the space of all n×n symmetricmatrices over the complex field F, and χ be an irreducible character of Sn and dχ the immanant associated with χ. The main objective of this paper is to prove that the maps Φ: Σn(F) → Σn(F) satisfying dχ(Φ(A) + αΦ(B)) = det(A + αB) for all singular matrices A, B ∈ Σn(F) and all scalars α ∈ F are linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on the set of all symmetric matrices.

KW - Determinant

KW - converters

KW - permanent

KW - symmetric matrices

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Converting immanants on singular symmetric matrices

Abstract

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Keywords

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