Abstract
We relate the category of sheaves on alcoves that was constructed in [FL1] to the representation theory of reductive algebraic groups. In particular, we show that its indecomposable projective objects encode the irreducible rational characters of a connected, semisimple and simply connected reductive algebraic group for characteristics above the Coxeter number.
Similar content being viewed by others
References
H. H. Andersen, J. C. Jantzen, W. Soergel, Representations of Quantum Groups at a pth Root of Unity and of Semisimple Groups in Characteristic p: Independence of p, Astérisque 220 (1994), 321 pp.
P. Fiebig, Sheaves on moment graphs and a localization of Verma flags, Adv. Math. 217 (2008), 683–712.
P. Fiebig, The combinatorics of Coxeter categories, Trans. Amer. Math. Soc. 360 (2008), 4211–4233.
P. Fiebig, The multiplicity one case of Lusztig’s conjecture, Duke Math. J. 153 (2010), 551–571.
P. Fiebig, Lusztig’s conjecture as a moment graph problem, Bull. London Math. Soc. 42(6) (2010), 957–972.
P. Fiebig, Sheaves on affine Schubert varieties, modular representations and Lusztig’s conjecture, J. Amer. Math. Soc. 24 (2011), 133–181.
P. Fiebig, M. Lanini, Sheaves on the alcoves and modular representations I, arXiv:1801.03959 (2018), to appear in Transform. Groups 25 (2020).
M. Lanini, Kazhdan–Lusztig combinatorics in the moment graph setting, J. Algebra 370 (2012), 152–170.
W. Soergel, Roots of unity and positive characteristic, in: Representations of Groups (Banff, AB, 1994), CMS Conf. Proc., Vol. 16, Amer. Math. Soc., Providence, RI, 1995, pp. 315–338.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
FIEBIG, P., LANINI, M. SHEAVES ON THE ALCOVES AND MODULAR REPRESENTATIONS II. Transformation Groups 25, 755–791 (2020). https://doi.org/10.1007/s00031-020-09562-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00031-020-09562-8