Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 53 min ago
Peer-reviewedCC BY 4.0International Mathematics Research Notices

Plethysm for characters of relative operads and props

  • Najib Idrissi
  • Erik Lindell
Open at sourcePDFCite

Abstract

We investigate the relationship between symmetric functions and the representation theory of operads, relative operads, and props. We extend the classical character map for symmetric sequences to relative bisymmetric sequences and symmetric bimodules. We introduce new operations on symmetric functions, the relative plethysm and the (connected) box product, which model via the character map the composition product of relative operads and the box product of prop(erad)s. As applications, we include the computation of characters for stable twisted cohomology of automorphism groups of free groups and the Albanese cohomology of the IA-automorphism group.

Related

  1. Restriction of p'-degree characters, fields of values, and relative normal complements
    David Cabrera-Berenguer
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Graphoid Automata, Frobenius PROPs, and Semiring Evaluation
    Antonios Kalampakas
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Cluster Algebras for Bosonic Plethysm
    Yelin Fan, Jiarui Fei
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  4. The h-expansion of the Plethysm hn[pr] and Polysymmetric Expansions in h⊗ and e⊗
    Aditya Khanna
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  5. Non-linear contexts and dependent operads
    El Mehdi Cherradi
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@article{idrissi2026plethysm,
  title = {{Plethysm for characters of relative operads and props}},
  author = {Najib Idrissi and Erik Lindell},
  journal = {International Mathematics Research Notices},
  year = {2026},
  month = sep,
  eprint = {2505.05910},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05061606v2},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Plethysm for characters of relative operads and props
AU  - Najib Idrissi
AU  - Erik Lindell
PY  - 2026
DA  - 2026/09/30
JO  - International Mathematics Research Notices
UR  - https://hal.science/hal-05061606v2
AB  - We investigate the relationship between symmetric functions and the representation theory of operads, relative operads, and props. We extend the classical character map for symmetric sequences to relative bisymmetric sequences and symmetric bimodules. We introduce new operations on symmetric functions, the relative plethysm and the (connected) box product, which model via the character map the composition product of relative operads and the box product of prop(erad)s. As applications, we include the computation of characters for stable twisted cohomology of automorphism groups of free groups and the Albanese cohomology of the IA-automorphism group.
SN  - 1073-7928
SN  - 1687-0247
ER  -