Skip to content
DraconiticResearch
Search Sources API
206,690 studies31 sourcesUpdated 36 min ago
PreprintarXiv licencearXiv

Constructing Casimirs for the quantum reflection equation

  • Erik Brodsky
  • Leonid O Chekhov
  • Quanyu Tang
Open at sourcePDFDOICite

Abstract

We explore the quantum reflection equation in the case of a full-dimensional n× n matrix 𝔸. Using the technique of q-determinants, we find closed expressions for the quantum Pfaffian (in the case of even n) and for new quantum Casimirs that are ratios of special quantum (Sklyanin) minors of 𝔸. Special attention is paid to the self-adjointness property of the newly constructed Casimirs. We put forward a conjecture that, adopting a natural ansatz for a quantum deformation of a Casimir of a classical algebra, self-adjointness implies commutativity. We also explore the relationship to networks of quantum cluster variables.

Related

  1. Commuting Families of Flag Quasideterminants in Reflection Equation Algebras of Type A
    Dmitry V. Talalaev
    arXivPreprintCC BY 4.0Full textMathematical physicsStatistical & nonlinear physicsarXiv
  2. Dual Reflection Groups from Solutions to the Yang--Baxter Equation
    Simon Crawford
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. A Column-Wise Reflection Method with Safeguarded Anderson Acceleration for the Continuous Sylvester Matrix Equation
    Yinglian Jin, Hailong Zhu, Wenyue Feng
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  4. On Constructing and Decoding Quantum Triorthogonal Codes
    Alessio Baldelli, Olai Å. Mostad, Hsuan-Yin Lin +2
    arXivPreprintarXiv licenceFull textGeneral mathematicsQuantum physics & quantum informationarXiv
  5. Coset Lifted Product Codes: Constructing Quantum LDPC Codes from Non-Normal Subgroup Actions
    Rajendra Prasad Rajpurohit, V. Lalitha, Shayan Srinivasa Garani
    arXivPreprintarXiv licenceFull textGeneral mathematicsQuantum physics & quantum informationarXiv

Cite

BibTeXRIS
BibTeX
@misc{brodsky2026constructing,
  title = {{Constructing Casimirs for the quantum reflection equation}},
  author = {Erik Brodsky and Leonid O Chekhov and Quanyu Tang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08796},
  eprint = {2611.08796},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08796},
}
RIS
TY  - UNPB
TI  - Constructing Casimirs for the quantum reflection equation
AU  - Erik Brodsky
AU  - Leonid O Chekhov
AU  - Quanyu Tang
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08796
UR  - https://arxiv.org/abs/2611.08796
AB  - We explore the quantum reflection equation in the case of a full-dimensional n× n matrix 𝔸. Using the technique of q-determinants, we find closed expressions for the quantum Pfaffian (in the case of even n) and for new quantum Casimirs that are ratios of special quantum (Sklyanin) minors of 𝔸. Special attention is paid to the self-adjointness property of the newly constructed Casimirs. We put forward a conjecture that, adopting a natural ansatz for a quantum deformation of a Casimir of a classical algebra, self-adjointness implies commutativity. We also explore the relationship to networks of quantum cluster variables.
ER  -