Tableaux and Orbit Harmonics for Transformation Monoids
Published:Dec 26, 2025 19:26
•1 min read
•ArXiv
Analysis
This paper extends existing representation theory results for transformation monoids, providing a characteristic-free approach applicable to a broad class of submonoids. The introduction of a functor and the establishment of branching rules are key contributions, leading to a deeper understanding of the graded module structures of orbit harmonics quotients and analogs of the Cauchy decomposition. The work is significant for researchers in representation theory and related areas.
Key Takeaways
- •Extends Grood's and Steinberg's results on representation theory.
- •Provides a characteristic-free approach applicable to submonoids containing the symmetric group.
- •Introduces a functor and establishes branching rules.
- •Describes graded module structures of orbit harmonics quotients.
- •Yields analogs of the Cauchy decomposition.
Reference
“The main results describe graded module structures of orbit harmonics quotients for the rook, partial transformation, and full transformation monoids.”