Quantized Coordinate Rings of the Unipotent Radicals of the Standard\n Borel Subgroups in SL_n+1

2013/10/28 by Andrew Jaramillo, Jaramillo, Andrew
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1310.7539

openalex publication_date 2013/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define two subalgebras which can be seen as the quantization of the\ncoordinate rings of the unipotent radical of the standard positive\n(respectively negative) Borel subgroup of SL_n+1. We give a presentation\nfor these algebras and show they are isomorphic. Moreover, we show that these\nalgebras are the conivariants of a natural O_q(T)-coaction on O_q(B^\±).\nFinally, using a dual pairing, we show that these algebras are isomorphic to\nthe quantum nilpotent Lie subalgebra of U_q( mathfraksl_n+1).\n

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