Holonomic modules for rings of invariant differential operators

Author(s)

Futorny, Vyacheslav ^{[1, 2]} ; Schwarz, Joao ^[1]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, Caixa Postal 66281, BR-05315970 Sao Paulo - Brazil

^[2] SUSTech, Int Ctr Math, Shenzhen - Peoples R China

• Document type: Journal article
• Source: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION; v. 31, n. 04, p. 605-622, JUN 2021.
• Web of Science Citations: 0

Abstract

We study holonomic modules for the rings of invariant differential operators on affine commutative domains with finite Krull dimension with respect to arbitrary actions of finite groups. We prove the Bernstein inequality for these rings. Our main tool is the filter dimension introduced by Bavula. We extend the results for the invariants of the Weyl algebra with respect to the symplectic action of a finite group, for the rings of invariant differential operators on quotient varieties, and invariants of certain generalized Weyl algebras under the linear actions. We show that the filter dimension of all above mentioned algebras equals 1. (AU)

• FAPESP's process: 18/18146-5 - Ore Domainas: localizations, invariants and representations.
• Grantee: João Fernando Schwarz
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 18/23690-6 - Structures, representations, and applications of algebraic systems
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants