Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Algethami, D., Mudrov, A.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G1973846972
OpenAlex ID: W7220448292