scientific article; zbMATH DE number 1131859

zbMath0964.17019MaRDI QIDQ4382848

Wolfgang Soergel

Publication date: 23 March 1998

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

characterscategory \({\mathcal O}\)affine Kac-Moody Lie algebraindecomposable tilting modulesKazhdan-Lusztig conjectures

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Representation theory for linear algebraic groups (20G05) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Quantum groups (quantized function algebras) and their representations (20G42)

Related Items (39)

Tensor ideals, Deligne categories and invariant theory ⋮ Quotients of representation rings ⋮ Parabolic Kazhdan-Lusztig polynomials for quasi-minuscule quotients ⋮ Dualities and derived equivalences for category \(\mathcal{O}\) ⋮ Applications of the category of linear complexes of tilting modules associated with the category \(\mathcal O\) ⋮ The Ringel dual of the Auslander-Dlab-Ringel algebra ⋮ The tilting tensor product theorem and decomposition numbers for symmetric groups. ⋮ Ringel duality and Auslander-Dlab-Ringel algebras ⋮ Generalized Blob Algebras and Alcove Geometry ⋮ Projective functors for algebraic groups. ⋮ Algebraic representations and constructible sheaves ⋮ Some homological properties of category \(\mathcal{O}\). IV ⋮ Alcove geometry and a translation principle for the Brauer algebra. ⋮ On minimal tilting complexes in highest weight categories ⋮ Parabolic Kazhdan-Lusztig \(R\)-polynomials for tight quotients of the symmetric groups. ⋮ Radically filtered quasi-hereditary algebras and rigidity of tilting modules ⋮ On the character of certain tilting modules ⋮ Projective-injective modules, Serre functors and symmetric algebras ⋮ Pseudocompact algebras and highest weight categories ⋮ Wall-Crossing functors and D-modules ⋮ Support varieties for quantum groups ⋮ On the category \(\mathcal O\) for rational Cherednik algebras. ⋮ On the structure of the blob algebra ⋮ Billiards and tilting characters for \(\mathrm{SL}_3\) ⋮ Parabolic Kazhdan-Lusztig \(R\)-polynomials for Hermitian symmetric pairs. ⋮ Categorification of (induced) cell modules and the rough structure of generalised Verma modules ⋮ Quotient Categories of Modular Representations ⋮ Kazhdan-Lusztig polynomials of Boolean elements ⋮ On the character of some modular indecomposable tilting modules for \(\text{SL}_3\) ⋮ Isomorphisms of Hecke modules and parabolic Kazhdan-Lusztig polynomials. ⋮ Semi-infinite cohomology and Hecke algebras ⋮ The Lascoux, Leclerc and Thibon algorithm and Soergel's tilting algorithm. ⋮ On Arkhipov's and Enright's functors. ⋮ Kazhdan-Lusztig polynomials, tight quotients and Dyck superpartitions. ⋮ Parabolic Kazhdan-Lusztig \(R\)-polynomials for quasi-minuscule quotients ⋮ Parabolic Kazhdan-Lusztig polynomials for Hermitian symmetric pairs ⋮ Generalized negligible morphisms and their tensor ideals ⋮ Iwahori-Hecke algebras of type \(A\) at roots of unity ⋮ A sum formula for tilting filtrations

Cites Work

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• Finite resolutions of modules for reductive algebraic groups
• On some geometric aspects of Bruhat orderings. II: The parabolic analogue of Kazhdan-Lusztig polynomials
• A decomposition theorem for certain self-dual modules in the category \(\mathcal O\)
• Projective modules over graded Lie algebras. I
• Structure of some categories of representations of infinite-dimensional Lie algebras
• Semi-infinite homological algebra
• The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences
• Tensor Structures Arising from Affine Lie Algebras. I
• On the differentials in the Lyndon-Hochschild-Serre spectral sequence
• Kazhdan-Lusztig-Polynome und eine Kombinatorik für Kipp-Moduln

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