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.
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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}
}
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33 pages