Converting immanants on singular symmetric matrices
- Authors: Duffner M.A.1, Guterman A.E.2,3
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Affiliations:
- Departamento de Matemática, Faculdade de Ciências
- Moscow State University
- Moscow Center for Continuous Mathematical Education
- Issue: Vol 38, No 4 (2017)
- Pages: 630-636
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/199575
- DOI: https://doi.org/10.1134/S1995080217040060
- ID: 199575
Cite item
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.
Keywords
About the authors
M. A. Duffner
Departamento de Matemática, Faculdade de Ciências
Author for correspondence.
Email: mamonteiro@fc.ul.pt
Portugal, Bloco C6, Piso 2, Campo Grande, Lisboa, 1700-016
A. E. Guterman
Moscow State University; Moscow Center for Continuous Mathematical Education
Email: mamonteiro@fc.ul.pt
Russian Federation, GSP-1, Moscow, 119991; Bolshoi Vlas’evskii per. 11, Moscow, 119002