2019/04/29 by Valentin Buciumas, Buciumas, Valentin, Hankyung Ko +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.CT #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.1904.12851
v2 corrects typos and misformulations in S8; v3 replaces S4, which contained an error; v4 the previous S8 is integrated in the rest of the paper because we can now prove proposition 2.6 (we thank Ruslan Maksimau and Catharina Stroppel for informing us of a lemma which lead to the proof). Other sections were also revised (ex S6.1, S7.3) v5: we incorporate referee suggestions throughout the paper
openalex publication_date 2019/04/29 · arxiv created 2020/01/23 · arxiv updated 2020/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a theory of two-parameter quantum polynomial functors. Similar to how (strict) polynomial functors give a new interpretation of polynomial representations of the general linear groups GLn, the two-parameter polynomial functors give a new interpretation of (polynomial) representations of the quantum symmetric pair (UQ,qB(\mathfrakgln), Uq(\mathfrakgln) ) which specializes to type AIII/AIV quantum symmetric pairs. The coideal subalgebra UQ,qB(\mathfrakgln) appears in a Schur-Weyl duality with the type B Hecke algebra \mathcal HBQ,q(d). We endow two-parameter polynomial functors with a cylinder braided structure which we use to construct the two-parameter Schur functors. Our polynomial functors can be precomposed with the quantum polynomial functors of type A producing new examples of action pairs.