Character formulas for tilting modules over Kac-Moody algebras

@article{Soergel1998CharacterFF,
  title={Character formulas for tilting modules over Kac-Moody algebras},
  author={Wolfgang Soergel},
  journal={Representation Theory of The American Mathematical Society},
  year={1998},
  volume={2},
  pages={432-448}
}
  • W. Soergel
  • Published 28 December 1998
  • Mathematics
  • Representation Theory of The American Mathematical Society
We show how to express the characters of tilting modules in a (possibly parabolic) category O over a Kac-Moody algebra in terms of the characters of simple highest weight modules. This settles, in lots of cases, Conjecture 7.2 of Kazhdan-Lusztig-Polynome and eine Kombinatorik für Kipp-Moduln, Representation Theory (An electronic Journal of the AMS) (1997), by the author, describing the character of tilting modules for quantum groups at roots 
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References

SHOWING 1-10 OF 16 REFERENCES
Semiinfinite cohomology of associative algebras and bar duality
We describe semiinfinite cohomology of associative algebras in terms of Koszul (or bar) duality. Consider an associative algebra $A$ and two its subalgebras $B$ and $N$ such that $A=B\otimes N$ as a
Infinite dimensional Lie algebras: Frontmatter
Semi-infinite homological algebra
SummaryThe paper provides a homological algebraic foundation for semi-infinite cohomology. It is proved that semi-infinite cohomology of infinite dimensional Lie algebras is a two-sided derived
Introduction to commutative algebra
* Introduction * Rings and Ideals * Modules * Rings and Modules of Fractions * Primary Decomposition * Integral Dependence and Valuations * Chain Conditions * Noetherian Rings * Artin Rings *
A Course in Homological Algebra
I. Modules.- 1. Modules.- 2. The Group of Homomorphisms.- 3. Sums and Products.- 4. Free and Projective Modules.- 5. Projective Modules over a Principal Ideal Domain.- 6. Dualization, Injective
...
...