Polynomial ring representations of endomorphisms of exterior powers

Abstract An explicit description of the ring rational polynomials in r indeterminates as a representation Lie algebra endomorphisms k -th exterior power countably infinite-dimensional vector space is given. Our based on results by Laksov and Throup concerning symmetric structure polynomial ring. are approximate versions vertex operators occurring celebrated bosonic representation, due to Date, Jimbo, Kashiwara Miwa, all matrices infinite size, whose entries zero but finitely many.