Recursive sequences attached to modular representations of finite groups
| Autor: | Alexandru Chirvasitu, Tara Hudson, Aparna Upadhyay |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Algebra and Number Theory
20C05 16D40 13F25 11K31 Mathematics::K-Theory and Homology Rings and Algebras (math.RA) FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) Group Theory (math.GR) Mathematics - Rings and Algebras Representation Theory (math.RT) Mathematics - Group Theory Mathematics - Representation Theory |
| Zdroj: | Journal of Algebra. 602:599-636 |
| ISSN: | 0021-8693 |
| Popis: | The core of a finite-dimensional modular representation $M$ of a finite group $G$ is its largest non-projective summand. We prove that the dimensions of the cores of $M^{\otimes n}$ have algebraic Hilbert series when $M$ is Omega-algebraic, in the sense that the non-projective summands of $M^{\otimes n}$ fall into finitely many orbits under the action of the syzygy operator $\Omega$. Similarly, we prove that these dimension sequences are eventually linearly recursive when $M$ is what we term $\Omega^{+}$-algebraic. This partially answers a conjecture by Benson and Symonds. Along the way, we also prove a number of auxiliary permanence results for linear recurrence under operations on multi-variable sequences. Comment: 30 pages + references |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect