Highest weight irreducible representations of the quantum algebra Uₕ(A∞)

الأصل · EN

A class of highest weight irreducible representations of the algebra Uₕ(A∞), the quantum analogue of the completion and central extension A∞ of the Lie algebra gl∞, is constructed. It is considerably larger than the known so far representations. Within each module a basis is introduced and the transformation relations of the basis under the action of the Chevalley generators are explicitly written. The verification of the quantum algebra relations to be satisfied is shown to reduce to a set of nontrivial q-number identities. All our representations are restricted in the terminology of S. Levendorskii and Y. Soibelman (Commun. Math. Phys. 140, 399-414 (1991)).