An observation on the determinant of a Sylvester-Kac type matrix

Abstract

Based on a less-known result, we prove a recent conjecture concerning the determinant of a certain Sylvester-Kac type matrix related to some Lie Algebras. The determinant of an extension of that matrix is presented.

Keywords

• sylvester-kac matrix
• clement matrix
• determinant
• eigenvalues
• lie algebras
• primary 15a18
• secondary 15a15