The Integral quantum loop algebra of \mathfrakgl_n

2014/04/23 by Jie Du, Qiang Fu, Du, Jie +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1404.5679

openalex publication_date 2014/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We will construct the Lusztig form for the quantum loop algebra of \mathfrakgl_n by proving the conjecture \cite[3.8.6]DDF and establish partially the Schur--Weyl duality at the integral level in this case. We will also investigate the integral form of the modified quantum affine \mathfrakgl_n by introducing an affine stabilisation property and will lift the canonical bases from affine quantum Schur algebras to a canonical basis for this integral form. As an application of our theory, we will also discuss the integral form of the modified extended quantum affine \mathfraksl_n and construct its canonical basis to verify a conjecture of Lusztig in this case.

Citations

• Quantum affine \frakgl_n via Hecke algebras
• BLM realization for the integral form of quantum \frakgl_n

Related

• Quantum affine \frakgl_n via Hecke algebras
• BLM realization for the integral form of quantum \frakgl_n
• Presenting quantum Schur algebras as quotients of the quantized universal enveloping algebra of gl(2)
• A Double Hall Algebra Approach to Affine Quantum Schur--Weyl Theory
• Embeddings among quantum affine \mathfraksl_n