An Algebra Associated with a Flag in a Subspace Lattice over a Finite Field and the Quantum Affine Algebra Uq(ŝl2)
نویسنده
چکیده
In this paper, we introduce an algebra H from a subspace lattice with respect to a fixed flag which contains its incidence algebra as a proper subalgebra. We then establish a relation between the algebra H and the quantum affine algebra Uq1/2(ŝl2), where q denotes the cardinality of the base field. It is an extension of the well-known relation between the incidence algebra of a subspace lattice and the quantum algebra Uq1/2(sl2). We show that there exists an algebra homomorphism from Uq1/2(ŝl2) to H and that any irreducible module for H is irreducible as an Uq1/2(ŝl2)-module. 2010 Mathematics Subject Classification: 51E20; 20G42
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