2024/09/05 by Ming Fang, Jun Hu, Fang, Ming +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2409.03379
openalex publication_date 2024/09/05 · openalex created_date 2024/10/19 · openalex updated_date 2026/07/28
Let g be a complex semisimple Lie algebra with Weyl group W. Let H(W) be the Iwahori-Hecke algebra associated to W. For each w∈ W, let Tw and Cw be the corresponding Z-graded twisting functor and Z-graded shuffling functor respectively. In this paper we present a categorical action of H(W) on the derived category Db(O0Z) of the Z-graded BGG category O0Z via derived twisting functors as well as a categorical action of H(W) on Db(O0Z) via derived shuffling functors. As applications, we get graded character formulae for TsL(x) and CsL(x) for each simple reflection s. We describe the graded shifts occurring in the action of the Z-graded twisting and shuffling functors on dual Verma modules and simple modules. We also characterize the action of the derived Z-graded Zuckerman functors on simple modules.