Remarks on quantum unipotent subgroups and the dual canonical basis

2015/06/25 by Yoshiyuki Kimura
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Basis (linear algebra) #Decomposition #Dual (grammatical number) #Geometry #Linguistics #Mathematical physics #Mathematics #Philosophy #Physics #Pure mathematics #Quantum #Quantum group #Quantum mechanics #Standard basis #Tensor (intrinsic definition) #Tensor product #Unipotent #Universal enveloping algebra #Weyl group #math.QA #math.RT

paper · pdf · doi:10.2140/pjm.2017.286.125

17 pages

arxiv created 2015/06/25 · arxiv updated 2016/12/13 · openalex publication_date 2016/12/14 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05

Abstract

We prove the tensor product decomposition of the half of quantized universal enveloping algebra associated with a Weyl group element which was conjectured by Berenstein and Greenstein.

Citations

• Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases
• On crystal bases of the Q-analogue of universal enveloping algebras
• Canonical Bases Arising from Quantized Enveloping Algebras