Center of Kostant algebra

2025/09/24 by Tamás Hausel, Hausel, Tamás
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2509.20159

openalex publication_date 2025/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, following Muić-Savin, we compute the center of Kostant algebra, introduced by Kostant in 1975 as strongly commuting algebra. We explain how it encodes information on tensor products between a finite-dimensional and a Verma module, and about the structure of principal series representations via the work of Bernstein-Gelfand. We also discuss conjectured relationships to Langlands duality.

Citations

• On Fourier-Mukai transforms of upward flows for Hitchin systems
• Descriptions of strongly multiplicity free representations for simple Lie algebras
• Enhanced mirror symmetry for Langlands dual Hitchin systems
• Endoscopic decompositions and the Hausel-Thaddeus conjecture
• Geometric stabilisation via p-adic integration
• Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration
• Modules for Relative Yangians (Family Algebras) and Kazhdan-Lusztig\n Polynomials
• Representations of complex semi-simple Lie groups and Lie algebras
• Global topology of the Hitchin system
• Langlands duality for Hitchin systems
• Le lemme fondamental pour les groupes unitaires

Related

• Kostant's problem for fully commutative permutations
• Kostant modules in blocks of category \mathcal O_S
• On the Kostant conjecture for Clifford algebra
• Kostant theorem for special filtered algebras
• Linear algebra meets Lie algebra: the Kostant-Wallach theory