Set Partitions, Fermions, and Skein Relations

DOI10.1093/imrn/rnac110zbMath1530.05194arXiv2109.06373MaRDI QIDQ6155929

Brendon Rhoades, Jesse Kim

Publication date: 7 June 2023

Published in: Séminaire Lotharingien de Combinatoire, International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.06373

zbMATH Keywords

exterior algebraskein relationnoncrossing set partition

Mathematics Subject Classification ID

Partitions of sets (05A18) Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Actions of groups on commutative rings; invariant theory (13A50) Group actions on combinatorial structures (05E18) Combinatorial aspects of groups and algebras (05E16)

Related Items (5)

A combinatorial basis for the fermionic diagonal coinvariant ring ⋮ A proof of the fermionic theta coinvariant conjecture ⋮ The combinatorics of supertorus sheaf cohomology ⋮ Quasisymmetric harmonics of the exterior algebra ⋮ An embedding of the skein action on set partitions into the skein action on matchings

Cites Work

• A skein action of the symmetric group on noncrossing partitions
• A combinatorial model for the decomposition of multivariate polynomial rings as \(S_n\)-modules
• Conjectures on the quotient ring by diagonal invariants
• The cyclic sieving phenomenon
• Harmonic differential forms for pseudo-reflection groups. I: Semi-invariants
• Theta operators, refined delta conjectures, and coinvariants
• A proof of the 4-variable Catalan polynomial of the delta conjecture
• Cyclic sieving of increasing tableaux and small Schröder paths
• A web basis of invariant polynomials from noncrossing partitions
• The invariant theory of binary forms
• Boolean Product Polynomials, Schur Positivity, and Chern Plethysm
• Vandermondes in superspace
• THE POLYTABLOID BASIS EXPANDS POSITIVELY INTO THE WEB BASIS
• The Transition Matrix between the Specht and Web Bases Is Unipotent with Additional Vanishing Entries

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