2023/12/21 by Cemile Kurkoglu, Kurkoglu, Cemile
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2312.14282
openalex publication_date 2023/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \bfG be a split connected reductive group over a finite extension F of \mathbb Qp, and let \bfT ⊂ \bfB ⊂ \bfG be a maximal split torus and a Borel subgroup, respectively. Denote by G = \bfG(F) and B= \bfB(F) their groups of F-valued points and by \mathfrak g = \rm Lie(G) and \mathfrak b = \rm Lie(B) their Lie algebras. Let \mathcal O^∞ be the thick category \mathcal O for (\mathfrak g,\mathfrak b), and denote by O^∞\rm alg ⊂ O^∞ the full subcategory consisting of objects whose weights are in X^*(\bfT). Both are Serre subcategories of the category of all U-modules, where U = U(\mathfrak g). We show first that the functor \mathbb D^\mathfrak g = \rm RHomU(-,U) preserves Db(U)_O^∞\rm alg, and we deduce from a result of Coulembier-Mazorchuk that the latter category is equivalent to Db(\mathcal O^∞\rm alg).