Work

Canonical bases and standard monomials

Year: 1998

Type: article

Abstract: Let U be the quantized enveloping algebra associated to a simple Lie algebra g by Drinfel'd and Jimbo. Let λ be a classical fundamental weight for g, and ⋯(λ) the irreducible, finite-dimensional type 1 highest weight U-module with highest weight λ. We show that the canonical basis for ⋯(λ) (see Kashiwara [6, §0] and Lusztig [18, 14.4.12]) and the standard monomial basis (see [11, §§2.4 and 2.5]) for ⋯(λ) coincide.

Source: Proceedings of the Edinburgh Mathematical Society

DOI: 10.1017/s0013091500019921

Author: R. J. Marsh

Institution: University of Glasgow

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: University of Warwick, Engineering and Physical Sciences Research Council

OpenAlex ID: W2159207196