2012/07/11 by Garrett Johnson, Johnson, Garrett, Christopher Nowlin +1
Mathematics · #16T20 #17B37 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16T20 #msc:17B37
paper · pdf · doi:10.48550/arxiv.1207.2605
15 pages
arxiv created 2012/07/11 · openalex publication_date 2012/07/11 · arxiv updated 2012/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
De Concini, Kac, and Procesi defined a family of subalgebras Uq[w] of the quantized enveloping algebra Uq(g) associated to elements w in the Weyl group of a simple Lie algebra g. These algebras are called quantum Schubert cell algebras. We show that, up to a mild cocycle twist, quotients of certain quantum Schubert cell algebras of types E6 and E6(1) map isomorphically onto distinguished subalgebras of the Faddeev-Reshetikhin-Takhtajan universal bialgebra associated to the braiding on the quantum half-spin representation of Uq(so10). We identify the quotients as those obtained by factoring out the quantum Schubert cell algebras by ideals generated by certain submodules with respect to the adjoint action of Uq(so10).