Work

Diamond representations of $\mathfrak{sl}(n)$

Year: 2005

Type: article

Abstract: In \cite{W}, there is a graphic description of any irreducible, finite dimensional $\mathfrak{sl}(3)$ module. This construction, called diamond representation is very simple and can be easily extended to the space of irreducible finite dimensional ${\mathcal U}\_q(\mathfrak{sl}(3))$-modules. In the present work, we generalize this construction to $\mathfrak{sl}(n)$. We show this is in fact a description of the reduced shape algebra, a quotient of the shape algebra of $\mathfrak{sl}(n)$. The basis used in \cite{W} is thus naturally parametrized with the so called quasi standard Young tableaux. To compute the matrix coefficients of the representation in this basis, it is possible to use Groebner basis for the ideal of reduced Plücker relations defining the reduced shape algebra.

Source: HAL (Le Centre pour la Communication Scientifique Directe)

DOI: 10.48550/arxiv.math/0507435

Authors: Arnal, Didier, Baraka, Nadia Bel, Wildberger, Norman J.

Institutions: Université de Bourgogne, Institut de Mathématiques de Bourgogne, UNSW Sydney

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W1973227305

FWCI:

Cites: 3

Cited by:

Related to: 10