Braid group action and quasi-split affine iquantum groups III

2025/11/02 by Ming Lu, Xiaolong Pan, Lu, Ming +5
Mathematics · #17B37 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2511.00882

openalex publication_date 2025/11/02 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28

Abstract

This is the last of three papers on Drinfeld presentations of quasi-split affine iquantum groups \widetilde\mathbf U^\imath, settling the remaining type \rm AIII^(τ)_2r. This type distinguishes itself among all quasi-split affine types in having 3 relative root lengths. Various basic real and imaginary v-root vectors for \widetilde\mathbf U^\imath are constructed, giving rise to affine rank one subalgebras of \widetilde\mathbf U^\imath associated with simple roots in the finite relative root system. We establish the relations among these v-root vectors and show that they provide a Drinfeld presentation of \widetilde\mathbf U^\imath.

Citations

• Quivers with Involutions and Shifted Twisted Yangians via Coulomb Branches
• Representations and characters of quantum affine algebras at the crossroads between cluster categorification and quantum integrable models
• Boundary q-characters of evaluation modules for split quantum affine symmetric pairs
• Braid group action and quasi-split affine \imathquantum groups I
• Factorisation of quasi K-matrices for quantum symmetric pairs
• Braid group action and root vectors for the q-Onsager algebra
• From the Drinfeld realization to the Drinfeld-Jimbo presentation of affine quantum algebras: the injectivity
• Braid group actions on coideal subalgebras of quantized enveloping\n algebras
• Hecke algebras with unequal parameters
• Coideal Subalgebras and Quantum Symmetric Pairs
• Boundary conditions for integrable quantum systems

Related

• Braid group action and quasi-split affine \imathquantum groups I
• Braid group action and quantum affine superalgebra for type \mathfrakosp(2m+1|2n)
• Morita invariants of quasitriangular comodule algebras
• iQuantum groups and iHopf algebras I: foundation
• Universal deformations of the finite quotients of the braid group on 3 strands