Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 53 min ago
PreprintarXiv licencearXiv

Further results on the paramodular Hecke algebra

  • Jennifer Johnson-Leung
  • Joshua Parker
  • Brooks Roberts
Open at sourcePDFDOICite

Abstract

In this paper we further examine the structure of the graded paramodular Hecke algebra ℋ. We define a commutative subring ℋα of ℋ as the elements fixed by a certain automorphism α, and we show that the elements T(qk), defined as the sum of the double cosets of degree k, are contained in ℋα. We prove that the formal power series in the indeterminate t with coefficients T(qk) is an explicit rational function in t with coefficients from ℋα. We also determine the structure of ℋα and its relation to ℋ.

Related

  1. Periodic ASEP and random walks on affine Hecke Algebra
    Alexey Bufetov, Nimisha Pahuja
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsProbabilityarXiv
  2. The Extension groups of one K-type representations of graded Hecke algebra
    Quanyong Chen
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Completed Iwahori–Hecke algebra for Kac–Moody groups over local fields
    Auguste Hébert, Dinakar Muthiah
    Proceedings of the London Mathematical SocietyPeer-reviewedCC BY 4.0Full textAlgebra & number theoryHAL
  4. Arithmetic Siegel-Weil for the spherical Hecke algebra
    Benjamin Howard
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. K-theory of Gieseker variety and type A cyclotomic Hecke algebra
    Vasily Krylov, Raphaël Paegelow, Pavel Shlykov
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{johnsonleung2026further,
  title = {{Further results on the paramodular Hecke algebra}},
  author = {Jennifer Johnson-Leung and Joshua Parker and Brooks Roberts},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07520},
  eprint = {2610.07520},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07520},
}
RIS
TY  - UNPB
TI  - Further results on the paramodular Hecke algebra
AU  - Jennifer Johnson-Leung
AU  - Joshua Parker
AU  - Brooks Roberts
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.07520
UR  - https://arxiv.org/abs/2610.07520
AB  - In this paper we further examine the structure of the graded paramodular Hecke algebra ℋ. We define a commutative subring ℋ^α of ℋ as the elements fixed by a certain automorphism α, and we show that the elements T(q^k), defined as the sum of the double cosets of degree k, are contained in ℋ^α. We prove that the formal power series in the indeterminate t with coefficients T(q^k) is an explicit rational function in t with coefficients from ℋ^α. We also determine the structure of ℋ^α and its relation to ℋ.
ER  -