2025/04/23 by Fernando Peña Vázquez, Vázquez, Fernando Peña
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Quantum Algebra (math.QA) #Representation Theory (math.RT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2504.16699
openalex publication_date 2025/04/23 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
We introduce the concept of a triangular decomposition for Banach and Fréchet-Stein algebras over p-adic fields, which allows us to define a category O for a wide array of topological algebras. In particular, we apply this concept to p-adic rational Cherednik algebras, which allows us to obtain an analytic version of the category O developed by Ginzburg, Guay, Opdam and Rouquier. Along the way, we study the global sections of p-adic Cherednik algebras on smooth Stein spaces, and determine their behavior with respect to the rigid analytic GAGA functor.