Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 12 min ago
PreprintarXiv licencearXiv

Laurent Symmetric Functions

  • Hugo Fernández
  • Elena Kleinwort
  • Tianze Li
  • Mario Torres-Danta
Open at sourcePDFDOICite

Abstract

We describe the ring of Laurent symmetric polynomials in terms of generators and relations, giving an analogue of the Fundamental Theorem of Symmetric Polynomials. We extend the Hall inner product, and give an algebraic proof that the Laurent Schur polynomials form an orthonormal basis of this ring. In the case of infinitely many variables, we realize the ring of Laurent symmetric functions as a direct limit of inverse limits, and relate them to characters of rational and algebraic representations of general linear groups.

Related

  1. Symmetric Branching via Laurent Phenomenon Algebras
    Jiarui Fei
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Closed formula for Kronecker structure constants of a molecular basis of homogeneous symmetric functions
    Josaphat W. V. Baolahy, Benjamin Randrianirina
    Enumerative Combinatorics and ApplicationsPeer-reviewedCC BY-NDFull textCombinatorics & discrete mathematicsDOAJ
  3. A zero-density estimate for the symmetric square L-functions in the weight aspect
    Songchen Yin
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Non-vanishing of symmetric square L-functions in the weight aspect
    Olga Balkanova, Dmitry Frolenkov
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. All minimum cuts of symmetric submodular functions
    Chao Xu
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsOptimisation & controlarXiv

Cite

BibTeXRIS
BibTeX
@misc{fernandez2026laurent,
  title = {{Laurent Symmetric Functions}},
  author = {Hugo Fernández and Elena Kleinwort and Tianze Li and Mario Torres-Danta},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15690},
  eprint = {2609.15690},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15690},
}
RIS
TY  - UNPB
TI  - Laurent Symmetric Functions
AU  - Hugo Fernández
AU  - Elena Kleinwort
AU  - Tianze Li
AU  - Mario Torres-Danta
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.15690
UR  - https://arxiv.org/abs/2609.15690
AB  - We describe the ring of Laurent symmetric polynomials in terms of generators and relations, giving an analogue of the Fundamental Theorem of Symmetric Polynomials. We extend the Hall inner product, and give an algebraic proof that the Laurent Schur polynomials form an orthonormal basis of this ring. In the case of infinitely many variables, we realize the ring of Laurent symmetric functions as a direct limit of inverse limits, and relate them to characters of rational and algebraic representations of general linear groups.
ER  -