2025/09/01 by Alexandru Chirvasitu, Chirvasitu, Alexandru
Mathematics · #14A15 #14L17 #14L30 #16D60 #16T05 #16T15 #18C40 #18M05 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2509.01386
openalex publication_date 2025/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X and \mathfraka be an affine scheme and (respectively) a finite-dimensional associative algebra over an algebraically-closed field \Bbbk, both equipped with actions by a linearly-reductive linear algebraic group G. We describe the simple finite-dimensional modules over the algebra of G-equivariant maps X→ \mathfraka in terms of the representation theory of the fixed-point subalgebras \mathfrakax:=\mathfrakaGx≤ \mathfraka, Gx being the respective isotropy groups of closed-orbit k-points x∈ X. This answers a question of E. Neher and A. Savage, extending an analogous result for (also linearly-reductive) finite-group actions. Moreover, the full category of finite-dimensional modules admits a direct-sum decomposition indexed by closed orbits.