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On Fusion Procedure For The Two-Parameter Quantum Algebra In Type A
by Naihuan Jing   Ming Liu

Vol. 14 No. 1 (2019) P.15~P.29
 DOI: https://doi.org/10.21915/BIMAS.2019102 10.21915/BIMAS.2019102

ABSTRACT

Finite dimensional irreducible modules of the two-parameter quantum enveloping algebra $U_{r,s}(\mathfrak{sl}_n)$ are explicitly constructed using the fusion procedure when $rs^{-1}$ is generic. This provides an alternative and combinatorial description of the Schur-Weyl duality for the two-parameter quantum linear algebras of type $A$.

KEYWORDS
Primary: 17B30; Secondary: 17B68.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: two-parameter quantum groups, fusion procedure, Schur-Weyl duality.

MILESTONES