An upper bound on the exceptional characteristics for Lusztig's character formula

By P. Fiebig. 2008

79 citations recorded by the source corpus.

Abstract We develop a Lefschetz theory in a combinatorial category associated to a root system and derive an upper bound on the exceptional characteristics for Lusztig's formula for the simple rational characters of a reductive algebraic group. Our bound is huge compared to the Coxeter number.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/26281344754f0023e6cde932bc0c7cfdf957ae4a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Simon Riche
2. David Savitt
3. F. Herzig
4. Shotaro Makisumi
5. Pramod N. Achar
6. C. Pillen
7. T. Gee
8. Brian J. Parshall

In Geometry and Topology

1. T. Gee
2. David Savitt
3. F. Herzig
4. Simon Riche
5. Brian J. Parshall
6. Shotaro Makisumi
7. Pramod N. Achar
8. C. Pillen

In Mathematical Physics

1. T. Gee
2. David Savitt
3. F. Herzig
4. Brian J. Parshall
5. Simon Riche
6. C. Pillen
7. Geordie Williamson
8. D. Nakano

Citations in the corpus

• Sheaves on affine Schubert varieties, modular representations and Lusztig's conjecture (2007, unknown): “In the papers [Fie06] and [Fie08c] we study the theory of sheaves on moment graphs, which gives the following alternative description of the indecomposable objects in H (cf. [Fie08b]).”
• Schubert calculus and torsion explosion (2013, methodology): “Fiebig also gives an explicit (enormous) bound [Fie12], which is exponential in the rank, and establishes the multiplicity one case [Fie10].”
• Tilting modules and the p-canonical basis (2015, background): “tig [KL] and Lusztig [L3], but only under the assumption that pis bigger than a non-explicit bound depending on the root system of G. TILTING MODULES AND THE p-CANONICAL BASIS 11 More recently Fiebig [F2] obtained an explicit bound above which the conjecture holds. However this bound is difficult to c”
• General Serre weight conjectures (2015, methodology): “h k · k as in Definition 3.3.4) into simple GLn(Fp)-modules. For p≫ 0, Lusztig’s conjecture allows one to recursively decompose Lλ ⊗Z p Fp into simple GLn-modules when λis p-regular ([Jan03, II.8.22], [Fie12]). For the remaining λone uses [Jan03, II.7.17(b)]. For decomposing simple GLn-modules as rep”
• Cohomology for Quantum Groups Via the Geometry of the Nullcone (2011, methodology): “he characters of the analogous irreducible modules for Uζ. This result has been proved by Andersen-Jantzen-Soergel [AJS] for all large p (no lower bound known except for small rank). Recently, Fiebig [Fie], improving upon the methods of [AJS], has provided a specific (large) bound on p for each root ”
• Koszul duality for Kac–Moody groups and characters of tilting modules (2017, background): “e assumption that ℓis larger than the Coxeter number [Lu1]. Lusztig’s conjecture was established for sufficiently large ℓ[AJS, KL2, Lu2, KT] and subsequently for ℓlarger than an explicit enormous bound [Fi]. On the other hand, ideas of Soergel, Elias, He, and the fourth author led to a uniform constru”