2018/11/30 by Taiki Shibata · 14 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algebraic group #Algebraic number #Algebraic structures and combinatorial models #Borel subgroup #Combinatorics #Euler characteristic #Field (mathematics) #Group (periodic table) #Mathematical analysis #Mathematics #Parameterized complexity #Pure mathematics #Simple (philosophy) #Structured program theorem #Supergroup #math.QA #math.RT #msc:14M30 #msc:16T05 #msc:17B10
paper · pdf · doi:10.1016/j.jalgebra.2019.11.019
published in Journal of Algebra 547, 179-219 (Elsevier BV) · 34 pages: The title have been changed. Some comments have been added. There are also some minor changes
arxiv created 2019/02/07 · openalex publication_date 2019/11/29 · arxiv updated 2020/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the structure of an algebraic supergroup \mathbbG and establish the Borel-Weil theorem for \mathbbG to give a systematic construction of all simple supermodules over an arbitrary field. Especially when \mathbbG has a distinguished parabolic super-subgroup, we show that the set of all simple supermodules of \mathbbG is parameterized by the set of all dominant weights for the even part of \mathbbG, prove a super-analogue of the Kempf vanishing theorem, and give a description of Euler characteristics.