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Graded twisted reflection matrices of GL-type

  • D. Algethami
  • A. Mudrov
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Abstract

We classify constant numerical solutions of the Z2-graded twisted reflection equation for the fundamental GL-type R-matrix and an arbitrary parity sequence, without assuming evenness or invertibility. The classification is based on a four-index locality principle established for this type of reflection equation. We determine the singular and invertible solutions and recover previously conjectured matrices for the minimal symmetric grading. Even invertible solutions comply with the recent classification of graded Satake diagrams. The classical stabilizer of a full-support lower-triangular non-even family is a Lie superalgebra whose even part is an electrical Lie algebra.

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Cite

BibTeXRIS
BibTeX
@misc{algethami2026graded,
  title = {{Graded twisted reflection matrices of GL-type}},
  author = {D. Algethami and A. Mudrov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02463},
  eprint = {2610.02463},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02463},
}
RIS
TY  - UNPB
TI  - Graded twisted reflection matrices of GL-type
AU  - D. Algethami
AU  - A. Mudrov
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.02463
UR  - https://arxiv.org/abs/2610.02463
AB  - We classify constant numerical solutions of the Z_2-graded twisted reflection equation for the fundamental GL-type R-matrix and an arbitrary parity sequence, without assuming evenness or invertibility. The classification is based on a four-index locality principle established for this type of reflection equation. We determine the singular and invertible solutions and recover previously conjectured matrices for the minimal symmetric grading. Even invertible solutions comply with the recent classification of graded Satake diagrams. The classical stabilizer of a full-support lower-triangular non-even family is a Lie superalgebra whose even part is an electrical Lie algebra.
ER  -