Tensor products of level zero representations

2000/12/14 by Vyjayanthi Chari, Chari, Vyjayanthi
Mathematics · #17B37 81R50 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B37 #msc:81R50

paper · pdf · doi:10.48550/arxiv.math/0012116

arxiv created 2000/12/14 · openalex publication_date 2000/12/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define an action of the braid group (associated with a simple Lie algebra) on the space of n-tuples of power series in an indeterminate u, with constant term zero. Using this, we give a sufficient condition for a tensor product of finite-dimensional representations of quantum affine algebras to be cyclic on the tensor product of highest weight vectors. In particular, this proves a generalization of a recently established conjecture of Akasaka and Kashiwara (see qa/0010293 and qa/0006084).

Citations

• Weyl Modules for Classical and Quantum Affine algebras

Related

• Braid Group Actions and Tensor Products
• Extremal loop weight modules and tensor products for quantum toroidal algebras
• Tensor product multiplicities for crystal bases of extremal weight modules over quantum infinite rank affine algebras of types B_∞, C_∞, and D_∞
• Tensor Product of the Fundamental Representations for the Quantum Loop Algebras of Type A at Roots of Unity
• Representations of Quantum Affinizations and Fusion Product