Canonical bases for the quantum linear supergroups

2014/10/03 by Jie Du, Haixia Gu, Du, Jie +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1410.0757

openalex publication_date 2014/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a combinatorial construction for the canonical bases of the ±-parts of the quantum enveloping superalgebra \bfU(\mathfrakgl_m|n) and discuss their relationship with the Kazhdan-Lusztig bases for the quantum Schur superalgebras \bsS(m|n,r) introduced in \citeDR. We will also extend this relationship to the induced bases for simple polynomial representations of \bfU(\mathfrakgl_m|n).

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