Irreducible representations of Lie algebras of reductive groups and the Kac-Weisfeiler conjecture

DOI10.1007/BF01884291zbMath0828.17008WikidataQ115393101 ScholiaQ115393101MaRDI QIDQ1895698

Alexander Premet

Publication date: 4 January 1996

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/144292

zbMATH Keywords

irreducible representationstrace formKac-Weisfeiler conjectureLie algebra of a connected reductive group

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Simple, semisimple, reductive (super)algebras (17B20) Lie algebras of linear algebraic groups (17B45) Modular Lie (super)algebras (17B50)

Related Items (52)

Factoriality for the reductive Zassenhaus variety and quantum enveloping algebra ⋮ On Kac-Weisfeiler modules for general and special linear Lie superalgebras ⋮ \(p\)-character of height one ⋮ The center of the enveloping algebra of the \(p\)-Lie algebras \(\mathfrak{sl}_{n}, \mathfrak{pgl}_{n}, \mathfrak{psl}_{n}\), when \(p\) divides \(n\) ⋮ Representations of quantum groups at roots of unity, Whittaker vectors and \(q\)-\(W\) algebras ⋮ Centers and Azumaya loci for finite W-algebras in positive characteristic ⋮ Homological aspects of Noetherian PI Hopf algebras and irreducible modules of maximal dimension ⋮ A generalization of Veldkamp's theorem for a class of Lie algebras ⋮ Invariants of centralisers in positive characteristic ⋮ One dimensional representations of finite \(W\)-algebras, Dirac reduction and the orbit method ⋮ Completions of symplectic reflection algebras. ⋮ The rank-one property for free Frobenius extensions ⋮ Representations of 𝔰𝔩3 in characteristic 3 ⋮ Modular representations in type \(A\) with a two-row nilpotent central character ⋮ Dimensions of modular irreducible representations of semisimple Lie algebras ⋮ A criterion for irreducibility of parabolic baby Verma modules of reductive Lie algebras ⋮ A note on Humphreys' conjecture on blocks ⋮ Generalized trace and modified dimension functions on ribbon categories ⋮ Representations of Lie superalgebras in prime characteristic. II: The queer series ⋮ Support varieties of semisimple-character representations for Cartan type Lie algebras ⋮ Finite \(W\)-superalgebras for queer Lie superalgebras ⋮ Enveloping algebras of Slodowy slices and Goldie rank ⋮ An analogue of the Kac-Weisfeiler conjecture ⋮ Finite \(W\)-superalgebras via super Yangians ⋮ Minimal \(W\)-superalgebras and the modular representations of basic Lie superalgebras ⋮ On irreducible representations of the Zassenhaus superalgebras with \(p\)-characters of height 0 ⋮ ON THE SMOOTHNESS OF CENTRES OF RATIONAL CHEREDNIK ALGEBRAS IN POSITIVE CHARACTERISTIC ⋮ Modular representations of Lie algebras of reductive groups and Humphreys' conjecture ⋮ A Morita theorem for modular finite \(W\)-algebras ⋮ Higher deformations of Lie algebra representations I. ⋮ Simple Lie algebras of small characteristic. VI: Completion of the classification ⋮ HIGHER DEFORMATIONS OF LIE ALGEBRA REPRESENTATIONS II ⋮ Conjugation in representations of the Zassenhaus algebra ⋮ Geometric representation theory of restricted Lie algebras ⋮ Block representation type of reduced enveloping algebras ⋮ Commutative quotients of finite \(W\)-algebras ⋮ Cohomology and support varieties for Lie superalgebras ⋮ An Analogue of the Jacobson-Morozov Theorem for Lie Algebras of Reductive Groups of Good Characteristics ⋮ Minimal-dimensional representations of reduced enveloping algebras for ⋮ Typical Blocks of Lie Superalgebras in Prime Characteristic ⋮ Mod-\(p\) reduction for quantum groups ⋮ Analogues of Weyl's Formula for Reduced Enveloping Algebras ⋮ Representation theory of the Witt algebra ⋮ A proof of the first Kac–Weisfeiler conjecture in large characteristics ⋮ Modular representations of simple Lie algebras ⋮ Special transverse slices and their enveloping algebras ⋮ On cocommutative Hopf algebras of finite representation type ⋮ Auslander-Reiten components for Lie algebras of reductive groups ⋮ Generalized reduced enveloping algebras for restricted Lie algebras ⋮ Finite \(W\)-superalgebras for basic Lie superalgebras ⋮ Dimensions of irreducible modules over \(W\)-algebras and Goldie ranks ⋮ Commuting varieties of Lie algebras over fields of prime characteristic

Cites Work

• Support varieties for restricted Lie algebras
• Geometry of p-unipotent Lie algebras
• Simple singularities and simple algebraic groups
• Representations of the Witt algebra
• Induction, deformation, and specialization of Lie algebra representations
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• The Lie algebras with a quotient trace form
• THE ZASSENHAUS VARIETY OF A CLASSICAL SEMISIMPLE LIE ALGEBRA IN FINITE CHARACTERISTIC
• Deformations of Lie Algebra Representations
• On Injective Modules for Infinitesimal Algebraic Groups, I
• IRREDUCIBLE REPRESENTATIONS OF THE LIE ALGEBRA $ \mathrm{sl}(n)$ OVER A FIELD OF POSITIVE CHARACTERISTIC
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• Quantum Coadjoint Action
• Conjugacy Classes in Parabolic Subgroups of Semisimple Algebraic Groups, II
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• On the Endomorphism Ring of a Simple Module Over an Enveloping Algebra
• Noncommutative Extensions of Hilbert Rings
• The Representations of Lie Algebras of Prime Characteristic
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