2017/03/31 by Anna Lachowska, You Qi · 1 citation
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Block (permutation group theory) #Center (category theory) #Cohomology #Dimension (graph theory) #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Quantum #Quantum group #Sheaf #math.AG #math.QA #math.RT #msc:14L99 #msc:17B37 #msc:20G05
paper · pdf · doi:10.1112/plms.12193
published as Proc. Lond. Math. Soc. (3) 118 (2019), no. 3, 513-544 · 36 pages, 3 figures, comments welcome. Minor corrections and updated references
openalex created_date 2017/03/16 · arxiv created 2018/09/12 · openalex publication_date 2018/09/13 · arxiv updated 2021/03/04 · openalex updated_date 2026/08/06
We generalize to the case of singular blocks the result in Bezrukavnikov and Lachowska [Quantum groups, Contemporary Mathematics 433 (American Mathematical Society, Providence, RI, 2007) 89–101] that describes the center of the principal block of a small quantum group in terms of sheaf cohomology over the Springer resolution. Then using the method developed in Lachowska and Qi [Int. Math. Res. Not., Preprint, 2017, arXiv:1604.07380], we present a linear algebro-geometric approach to compute the dimensions of the singular blocks and of the entire center of the small quantum group associated with a complex semisimple Lie algebra. A conjectural formula for the dimension of the center of the small quantum group at an lth root of unity is formulated in type A.