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Everything about Generalized Verma module
In mathematics, generalized Verma modules are a generalization of a (true) Verma module, and are objects in the representation theory of Lie algebras. They were studied originally by James Lepowsky in the 1970s. The motivation for their study is that their homomorphisms correspond to invariant differential operators over generalized flag manifolds. The study of these operators is an important part of the theory of parabolic geometries. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Generalized Verma moduleA 5-minute orientation
- Skim a recent paper: Gelfand–Kirillov Dimension and Reducibility of Scalar Generalized Verma Modules for Classical Lie AlgebrasInfluential work since 2022
- Pick up a classic book: Hodge theory, complex geometry, and representation theoryThe most-reprinted book on the subject
- Read the landmark paper: Generalized Verma modules, loop space cohomology and MacDonald-type identitiesCited 55 times
- Go sideways: Verma moduleA closely related topic
- Go sideways: Harish-Chandra isomorphismA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Generalized Verma modules, loop space cohomology and MacDonald-type identities
The Kazhdan-Lusztig conjecture for generalized Verma modules
Restrictions of generalized Verma modules to symmetric pairs
Verma modules over generalized Virasoro algebras Vir[G]
Verma modules over generalized Witt algebras
Automorphisms and Verma modules for generalized Schrödinger–Virasoro algebras
Homomorphisms between generalized Verma modules
Tableaux Realization of Generalized Verma Modules
🆕 Influential since 2022
Gelfand–Kirillov Dimension and Reducibility of Scalar Generalized Verma Modules for Classical Lie Algebras
Generalized imaginary Verma and Wakimoto modules
Reducibility of Scalar Generalized Verma Modules of Minimal Parabolic Type
Faithfulness of generalised Verma modules for Iwasawa algebras
On the reducibility of scalar generalized Verma modules of Hermitian type
đź“š Books worth reading
Hodge theory, complex geometry, and representation theoryNSF/CBMS Regional Conference in the Mathematical Sciences: Hodge Theory, Complex Geometry, and Representation Theory (2012 Fort Worth, Tex.) · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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