Explicit constructions of the fundamental representations of the symplectic Lie algebras (Q5925792)

The paper deals with the fundamental representations of the symplectic Lie algebra \(\mathfrak g = \mathfrak s\mathfrak p(2n,\mathbb{C})\). The author explicitly specifies the matrix entries for the representing matrices of generators of \(\mathfrak g\) with respect to each of the two explicit bases. The idea is to use a family of partially ordered sets to describe the actions of the generators of \(\mathfrak g\) on a specified basis. The symplectic columns of De Concini and of Kashiwara and Nakashima are used for the constructions. Quantum versions of the constructions used are also considered.