English

Totally nonnegative Peterson variety and strongly dominant weight polytope

Algebraic Geometry 2025-12-09 v1 Combinatorics Representation Theory

Abstract

We study the totally nonnegative part of the Peterson variety in arbitrary Lie type and establish its connection to the strongly dominant weight polytope. In particular, we prove that the totally nonnegative part of the Peterson variety is a regular CW-complex, which is homeomorphic to a cube as a cell-decomposed space. This confirms a conjecture of Rietsch for all Lie types.

Keywords

Cite

@article{arxiv.2512.06646,
  title  = {Totally nonnegative Peterson variety and strongly dominant weight polytope},
  author = {Hiraku Abe and Tao Gui and Haozhi Zeng},
  journal= {arXiv preprint arXiv:2512.06646},
  year   = {2025}
}

Comments

33 pages