A computer algorithm for the BGG resolution

DOI10.1016/j.jalgebra.2020.09.043zbMath1471.17037arXiv1911.00871OpenAlexW2984802640MaRDI QIDQ2216568

Nicolas Hemelsoet, Rik Voorhaar

Publication date: 16 December 2020

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

Full work available at URL: https://arxiv.org/abs/1911.00871

zbMATH Keywords

flag varietiesBGG resolution

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Grassmannians, Schubert varieties, flag manifolds (14M15) Homological methods in Lie (super)algebras (17B55) Computational methods for problems pertaining to nonassociative rings and algebras (17-08) Software, source code, etc. for problems pertaining to nonassociative rings and algebras (17-04)

Related Items (4)

bgg-cohomology ⋮ On certain Hochschild cohomology groups for the small quantum group ⋮ Hochschild cohomology of generalised Grassmannians ⋮ Polyvector fields for Fano 3-folds

Uses Software

• FLINT
• IML - Integer Matrix Library
• PARI/GP
• SageMath
• GitHub

Cites Work

• BGG resolutions via configuration spaces
• Homogeneous vector bundles
• Homomorphisms of the modules \(M_\chi\)
• Singular vectors in Verma modules over Kac-Moody algebras
• The Hochschild cohomology ring of a global quotient orbifold
• Differential equations and singular vectors in Verma modules over \(\mathfrak{sl}(n, \mathbb{C})\)
• Splitting Criteria for -Modules Induced from a Parabolic and the Bernstein-Gelfand-Gelfand Resolution of a Finite Dimensional, Irreducible -Module
• The Center of Small Quantum Groups I: The Principal Block in Type A
• A BLAS based C library for exact linear algebra on integer matrices
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