Positivity and the canonical basis of tensor products of finite-dimensional irreducible representations of quantum sl(k)

2008/04/12 by Joshua Sussan, Sussan, Joshua
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0804.2034

openalex publication_date 2008/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a categorification of tensor products of fundamental representations of quantum sl(k) via highest weight categories, the indecomposable tilting modules descend to the canonical basis. Since projective functors map tilting modules to tilting modules, the coefficients of the canonical basis of tensor products of finite dimensional, irreducible representations under the action of the Chevalley generators are positive.

Related

• Canonical bases of tensor products of integrable highest weight modules arising from framed constructions
• Module categories over representations of SL_q(2) in the non-semisimple case
• Positivity properties of canonical bases
• Tensor ideals for quantum groups via minimal tilting complexes
• Tensor products and q-characters of HL-modules and monoidal categorifications