A construction of irreducible \(\text{GL}(m)\) representations (Q5954566)

Let \(E\) be a finite dimensional vector space over a field \(K\). \textit{W. Fulton} presented an elegant description of irreducible \(\text{GL}(E)\)-modules when \(K\) is of characteristic \(0\), a treatment that combines the classical approach in terms of products of determinants with a functorial approach in Chap. 8 of his book [Young tableaux. With applications to representation theory and geometry, Lond. Math. Soc. Stud. Texts, 35, Cambridge Univ. Press, Cambridge (1997; Zbl 0878.14034)].NEWLINENEWLINENEWLINEIn this paper the author presents a similar approach with exterior powers replaced by symmetric powers. It requires considering exterior algebra indeterminates instead of polynomial indeterminates and leads to a new construction of irreducible \(\text{GL}(m)\)-modules. A combination of both approaches can be used to construct in the same vein tensor representations of general linear Lie superalgebras.