Tensor powers of vector representation of U_q(\mathfraksl₂) at even roots of unity

2024/04/05 by Anna Lachowska, Lachowska, Anna, Olga Postnova +5
Mathematics · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #FOS: Mathematics #Representation Theory (math.RT) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2404.03933

openalex publication_date 2024/04/05 · openalex created_date 2024/04/09 · openalex updated_date 2026/07/28

Abstract

We study the decomposition of tensor powers of two dimensional irreducible representations of quantum \mathfraksl₂ at even roots of unity into direct sums of tilting modules. We derive a combinatorial formula for multiplicity of tilting modules in the N-th tensor power of two dimensional irreducible representations, interpret it in terms of lattice paths and find its asymptotic behavior when N→∞. We also describe the limit of character and Plancherel measures when N→∞. We consider both U_q(\mathfraksl₂) with divided powers and the small quantum sl₂.

Related

• Combinatorial insights on tensor power decomposition in U_q(\mathfraksl₂)-module
• Growth Problems of Quantum Groups
• Dimensions of quantized tilting modules
• Structure of the tensor product of two simple modules of quantum GL₂
• Signatures of Multiplicity Spaces in tensor products of \mathfraksl₂ and U_q(\mathfraksl₂) Representations