Totally nonnegative Peterson variety and strongly dominant weight polytope
Hiraku Abe, Tao Gui, and Haozhi Zeng
TL;DR
This paper explores the totally nonnegative part of the Peterson variety across all Lie types, proving it forms a regular CW-complex homeomorphic to a cube, confirming Rietsch's conjecture.
Contribution
It establishes the topological structure of the totally nonnegative Peterson variety as a cube-shaped CW-complex for all Lie types, confirming a longstanding conjecture.
Findings
The totally nonnegative Peterson variety is a regular CW-complex.
It is homeomorphic to a cube as a cell-decomposed space.
The result holds for arbitrary Lie types.
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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Taxonomy
TopicsHolomorphic and Operator Theory · Algebraic Geometry and Number Theory · Geometry and complex manifolds