Combinatorial insights on tensor power decomposition in U_q(\mathfraksl₂)-module

2023/07/20 by Vinit Sinha, Sinha, Vinit
Computer Science · Mathematics · #17B37 #20G42 #Algebraic structures and combinatorial models #Coding theory and cryptography #FOS: Mathematics #Quantum Algebra (math.QA) #Quantum Computing Algorithms and Architecture #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2307.10840

openalex publication_date 2023/07/20 · openalex created_date 2023/07/22 · openalex updated_date 2026/07/28

Abstract

Let V(1) be the natural representation of U(\mathfraksl₂). The multiplicities of V(k) in V(1)^{⊗ N} have multiple interpretations in combinatorics. In this paper, we investigate one such combinatorial interpretation of their multiplicities. Furthermore, we extend our analysis to the two-dimensional representation T(1) of the restricted quantum enveloping algebra U_q^res(\mathfraksl₂). By employing combinatorial techniques, this study aims to elucidate the multiplicity of T(k) within T(1)^{⊗ N} while also offering a comprehensive analysis of the asymptotic behavior of these multiplicities as the parameter N approaches infinity.

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