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On Kac parameters and spectral decomposition of a matrix of specialized roots of Lie algebra $\mathfrak{;; ; sl};; ; _n$

This paper presents interesting spectral properties of a particular integer skew-symmetric matrix, used to encode information on $\mathbb{; ; ; Z}; ; ; $-gradation of type $\mathbf{; ; ; \tilde{; ; ; s}; ; ; }; ; ; $ for classical affine Lie algebra $\widetilde{; ; ; \mathfrak{; ; ; sl}; ; ; }; ; ; _n$. It is shown that the hidden Kac parameters can be revealed using an explicitly computed eigenvector in a Gram-Schmidt orthogonalization process.

$\mathbb{; ; ; Z}; ; ; $-gradation for classical (affine) Lie algebra ; Kac parameters of finite order automorphisms of simple Lie algebras ; Matrix of specialized roots ; Integer skew-symmetric matrix ; Spectral decomposition.

AMS subject classifications: 17B67, 15A18, 15B57 Pridruženi projekti su HRZZ-2634 i HRZZ-9345