2024/04/16 by Sam Jeralds, Jeralds, Sam · 1 citation
Mathematics · #14F43 #14M15 #17B10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2404.10266
openalex publication_date 2024/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a simple, simply-connected complex algebraic group with Lie algebra \mathfrakg, and G/B the associated complete flag variety. The Hochschild cohomology HH^\bullet(G/B) is a geometric invariant of the flag variety related to its generalized deformation theory and has the structure of a \mathfrakg-module. We study this invariant via representation-theoretic methods; in particular, we give a complete list of irreducible subrepresentations in HH^\bullet(G/B) when G=SLn(ℂ) or is of exceptional type (and conjecturally for all types) along with nontrivial lower bounds on their multiplicities. These results follow from a conjecture due to Kostant on the structure of the tensor product representation V(ρ) ⊗ V(ρ).