Based morphisms for characters of quantum symmetric pairs

2025/10/20 by Stein Meereboer, Meereboer, Stein
Mathematics · Physics and Astronomy · #17B37 #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Quantum Algebra (math.QA) #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.2510.17655

openalex publication_date 2025/10/20 · openalex created_date 2025/10/22 · openalex updated_date 2026/07/28

Abstract

We study based one-dimensional modules of quantum symmetric pairs over the field ℚ(q). We provide a complete classification of one-dimensional B-modules that appear as submodules of simple finite-dimensional based U-modules and determine the corresponding branching rules. The main result of this paper shows that the corresponding projections are morphisms of based B-modules. To this end we characterize one-dimensional modules at q=∞, thus developing a \imathcrystal basis theory for these modules. This is then applied to show compatibility with the integral forms of the (dual-)canonical basis.

Citations

• Quantum spherical functions of type χ as Macdonald-Koornwinder polynomials
• Integrable modules over quantum symmetric pair coideal subalgebras
• Symmetries for spherical functions of type χ for quantum symmetric pairs
• Coordinate rings on symmetric spaces
• Universal K-matrix for quantum symmetric pairs

Related

• Crystal basis theory for a quantum symmetric pair (U,U^\jmath)
• Boundary q-characters of evaluation modules for split quantum affine symmetric pairs
• Based modules over the \imathquantum group of type AI
• Global crystal bases for integrable modules over a quantum symmetric pair of type AIII
• Crystal bases for the quantum queer superalgebra