Determinants and Algebraic Identities Associated with the Root Systems of Classical Lie Algebras

Abstract

By means of the Laplace expansion formula, we establish a general theorem concerning determinants and algebraic sums. Its combinations with the determinants associated with the root systems of classical Lie algebras lead us to several striking algebraic identities, including a couple of those due to Gustafson and Milne [8].

Key Words:

• Classical root systems
• Symmetric function
• Vandermonde determinant

2010 Mathematics Subject Classification:

• Primary 05E05
• Secondary 15A15

Notes

Communicated by V. A. Artamonov.