Categorification of tensor powers of the vector representation of\n U_q( mathfrakgl(1|1))

2013/05/27 by Antonio Sartori, Sartori, Antonio · 1 citation
Mathematics · #17B10 (Primary) #17B37 #20C08 (Secondary) #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.1305.6162

openalex publication_date 2013/05/27 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

We consider the monoidal subcategory of finite dimensional representations of\nU_q( mathfrakgl(1|1)) generated by the vector representation, and we\nprovide a diagram calculus for the intertwining operators, which allows to\ncompute explicitly the canonical basis. We construct then a categorification of\nthese representations and of the action of both U_q( mathfrakgl(1|1)) and\nthe intertwining operators using subquotient categories of the BGG category\n\O( mathfrakgl_n).\n

Citations

• 2-Kac-Moody algebras

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