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D. Kazhdan, G. Lusztig (1979)
Representations of Coxeter groups and Hecke algebrasInventiones mathematicae, 53
D. Kazhdan, G. Lusztig (1993)
Tensor structures arising from affine Lie algebras. IIIJournal of the American Mathematical Society, 6
W. Soergel (2004)
KAZHDAN-LUSZTIG-POLYNOME UND UNZERLEGBARE BIMODULN ÜBER POLYNOMRINGENJournal of the Institute of Mathematics of Jussieu, 6
H. Andersen, J. Jantzen, W. Soergel (1994)
Representations of quantum groups at a p-th root of unity and of semisimple groups in characteristic p : independence of pAstérisque, 220
J. Humphreys (1971)
Modular representations of classical Lie algebras and semisimple groupsJournal of Algebra, 19
P. Fiebig (2005)
The combinatorics of Coxeter categoriesTransactions of the American Mathematical Society, 360
W. Soergel (1997)
Kazhdan-Lusztig-Polynome und eine Kombinatorik für Kipp-ModulnRepresentation Theory of The American Mathematical Society, 1
P. Fiebig (2006)
The multiplicity one case of Lusztig's conjectureDuke Mathematical Journal, 153
(1980)
Math. Soc. Providence, R.I
小竹 武 (1981)
Geometry of the Laplace operator
(1994)
Roots of unity and positive characteristic, Representations of groups (Banff, AB
P. Fiebig (2006)
Multiplicity one results in Kazhdan-Lusztig theory and equivariant intersection cohomology
M. Kaneda (1988)
The Kazhdan-Lusztig polynomials arising in the modular representation theory of reductive algebraic groups(Combinatorial Theory and Related Topics : Mutual Relation among Commutative Algebra,Algebraic Geometry,Representation Theory of Lie Algebras and Partially Ordered Sets)
P. Fiebig (2007)
Sheaves on affine Schubert varieties, modular representations and Lusztig's conjecturearXiv: Representation Theory
G. Lusztig (1980)
Hecke algebras and Jantzen's generic decomposition patternsAdvances in Mathematics, 37
Tom Braden, R. Macpherson (2000)
From moment graphs to intersection cohomologyMathematische Annalen, 321
Universität Freiburg, 79104 Freiburg, Germany E-mail address: peter.fiebig@math.uni-freiburg
D. Kazhdan, G. Lusztig (1980)
Schubert varieties and Poincar'e duality
M. Kaneda (1987)
On the inverse Kazhdan-Lusztig polynomials for affine Weyl groups.Journal für die reine und angewandte Mathematik (Crelles Journal), 1987
M. Kashiwara, T. Tanisaki (1995)
Kazhdan-Lusztig conjecture for affine Lie algebras with negative levelDuke Mathematical Journal, 77
P. Fiebig (2008)
An upper bound on the exceptional characteristics for Lusztig's character formula, 2012
R. Steinberg (1963)
Representations of Algebraic GroupsNagoya Mathematical Journal, 22
(1993)
J. Amer. Math. Soc. J. Amer. Math. Soc. J. Amer. Math. Soc
B. Parshall (1982)
Modular Representations of Algebraic Groups
P. Fiebig (2005)
Sheaves on moment graphs and a localization of Verma flagsAdvances in Mathematics, 217
(1986)
Simulating algebraic geometry with algebra. III. The Lusztig conjecture as a T G 1 -problem
B. Cooperstein, G. Mason (1981)
The Santa Cruz Conference on Finite Groups, 37
G. Lusztig (1979)
Some problems in the representation theory of nite Cheval-ley groups
S. Kato (1985)
On the Kazhdan-Lusztig polynomials for affine Weyl groupsAdvances in Mathematics, 55
We survey a new approach towards Lusztig's conjecture on the irreducible characters of a reductive algebraic group over a field of positive characteristic. The main result that we review is that Lusztig's conjecture is implied by a multiplicity conjecture on the stalks of certain sheaves on a moment graph. This latter conjecture is known to hold if the underlying field is of characteristic 0. From this one can almost directly deduce the conjecture for fields of large enough characteristics; but using a Lefschetz‐type theory on the moment graph, we can give an upper bound on the exceptions. Moreover, one can prove the multiplicity 1 case of the conjecture in full generality. In addition to a survey of the above results, we prove the equivalence between the original conjecture of Lusztig and its generic version, that is, the multiplicity conjecture for baby Verma modules for the corresponding Lie algebra.
Bulletin of the London Mathematical Society – Wiley
Published: Dec 1, 2010
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