2015/05/14 by L. Frappat, Luc Frappat, Naihuan Jing +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Affine Lie algebra #Affine representation #Affine transformation #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Cellular algebra #Center (category theory) #Current algebra #Homomorphism #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum #Quantum affine algebra #Quantum mechanics #Realization (probability) #Type (biology) #math-ph #math.MP #math.QA #math.RT
paper · pdf · doi:10.1007/s00220-015-2566-7
published as Commun. Math. Phys. 345 (2016), 631-657 · 32 pages
arxiv created 2015/05/14 · openalex publication_date 2016/01/11 · arxiv updated 2016/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give explicit formulas for the elements of the center of the completed quantum affine algebra in type A at the critical level which are associated with the fundamental representations. We calculate the images of these elements under a Harish-Chandra-type homomorphism. These images coincide with those in the free field realization of the quantum affine algebra and reproduce generators of the q-deformed classical W-algebra of Frenkel and Reshetikhin.