Multiplicity free categories of highest weight representations

DOI10.1080/00927879008823953zbMath0757.17005OpenAlexW2143712920MaRDI QIDQ4712924

Brian D. Boe, David H. Collingwood

Publication date: 25 June 1992

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879008823953

zbMATH Keywords

complex simple Lie algebraHermitian symmetric pairreal rank onemultiplicity free categoriesrelative Verma modulesunique Loewy filtration

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Homological methods in Lie (super)algebras (17B55) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items (9)

Lowest weight modules of \(\mathrm{Sp}_4 (\mathbb{R})\) and nearly holomorphic Siegel modular forms ⋮ Generalised Jantzen filtration of exceptional Lie superalgebras ⋮ Generalized Verma modules over \(U_q(\mathfrak{sl}_n(\mathbb{C}))\) ⋮ The homomorphisms between scalar generalized Verma modules associated to maximal parabolic subalgebras ⋮ Koszul duality for extension algebras of standard modules. ⋮ Diagrammatic description for the categories of perverse sheaves on isotropic Grassmannians ⋮ Unnamed Item ⋮ Invariant local twistor calculus for quaternionic structures and related geometries ⋮ On the homomorphisms between scalar generalized Verma modules

Cites Work

• Classification of irreducible tempered representations of semisimple groups. I
• A multiplicity one theorem for holomorphically induced representations
• A comparison theory for the structure of induced representations
• The Kazhdan-Lusztig conjecture for generalized Verma modules
• On some geometric aspects of Bruhat orderings. II: The parabolic analogue of Kazhdan-Lusztig polynomials
• Kazhdan-Lusztig conjecture and holonomic systems
• Classical Bruhat orders and lexicographic shellability
• Representations of Coxeter groups and Hecke algebras
• Über primitive Ideale in der Einhüllenden einer halbeinfachen Lie- Algebra
• Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren
• Tensor products of finite and infinite dimensional representations of semisimple Lie groups
• Irreducible characters of semisimple Lie groups. I
• Graded characters of induced representations for real reductive Lie groups. I
• A comparison theory for the structure of induced representations. II
• Hecke algebras and characters of parabolic type of finite groups with (B, N)-pairs
• Filtrations on generalized Verma modules for Hermitian symmetric pairs.

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