Whittaker categories and the minimal nilpotent finite \(W\)-algebras for \(\mathfrak{sl}_{n+1}\)

DOI10.1007/s00209-024-03469-warXiv2304.08791OpenAlexW4393205325MaRDI QIDQ6193763

Genqiang Liu, Yang Li

Publication date: 19 March 2024

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2304.08791

zbMATH Keywords

quiverWhittaker modulefinite \(W\)-algebracuspidal module

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Universal enveloping (super)algebras (17B35) Structure theory for Lie algebras and superalgebras (17B05) Simple, semisimple, reductive (super)algebras (17B20)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On weight modules of algebras of twisted differential operators on the projective space
• Blocks and modules for Whittaker pairs
• Finite-dimensional representations of \(W\)-algebras
• Cuspidal \(\mathfrak{sl}_n\)-modules and deformations of certain Brauer tree algebras
• Irreducible modules over the Virasoro algebra
• Shifted Yangians and finite \(W\)-algebras
• \(\mathcal{U}(\mathfrak{h})\)-free modules and coherent families
• Whittaker modules for the affine Lie algebra \(A_1^{(1)}\)
• Whittaker modules for Heisenberg algebras and imaginary Whittaker modules for affine Lie algebras
• Cuspidal representations of \(\mathfrak{sl}(n+1)\)
• On modules induced from Whittaker modules
• Blocks of tame representation type and related algebras
• On Whittaker vectors and representation theory
• The composition series of modules induced from Whittaker modules
• Irreducible Witt modules from Weyl modules and \(\mathfrak{gl}_n\)-modules
• Special transverse slices and their enveloping algebras
• Complete reducibility of torsion free \(C_n\)-modules of finite degree
• Classification of irreducible weight modules
• Quantization and injective submodules of differential operator modules
• Exponentiation and Fourier transform of tensor modules of \(\mathfrak{sl}(n+1)\)
• On Whittaker modules for a Lie algebra arising from the 2-dimensional torus
• Whittaker modules for the twisted affine Nappi-Witten Lie algebra \(\widehat{H}_4 [\tau\)]
• Enveloping algebras of Slodowy slices and the Joseph ideal
• Whittaker modules for \(U_q(\mathfrak{sl}_2)\)
• Sur les corps liés aux algèbres enveloppantes des algèbres de Lie
• Whittaker Categories for the Virasoro Algebra
• Classification of finite-dimensional irreducible modules over -algebras
• Highest weight categories arising from Khovanov’s diagram algebra III: category 𝒪
• Derived subalgebras of centralisers and finite -algebras
• Lie Algebra Modules with Finite Dimensional Weight Spaces, I
• Whittaker modules for generalized Weyl algebras
• WHITTAKER MODULES FOR THE VIRASORO ALGEBRA
• Finite-dimensional representations of minimal nilpotent W-algebras and zigzag algebras
• Affine Lie algebra representations induced from Whittaker modules
• Whittaker modules for the super-Virasoro algebras
• Twisted Harish–Chandra Sheaves and Whittaker Modules: The Nondegenerate Case
• INDECOMPOSABLE REPRESENTATIONS OF THE LORENTZ GROUP
• Introduction to Lie Algebras and Representation Theory
• On Some Applications of the Universal Enveloping Algebra of a Semisimple Lie Algebra
• A Whittaker category for the symplectic Lie algebra and differential operators
• One dimensional representations of finite \(W\)-algebras, Dirac reduction and the orbit method
• Classical Whittaker modules for the classical affine Kac-Moody algebras