5 papers
Structure constants of Peterson Schubert calculus
Tao Gui, Yuqi Jia, Xinkai Yu +2
We give an explicit, positive, and type-uniform formula for all equivariant structure constants of the Peterson Schubert calculus in arbitrary Lie types, using only the Cartan matr…
Totally nonnegative Peterson variety and strongly dominant weight polytope
Hiraku Abe, Tao Gui, Haozhi Zeng
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 t…
UniPaint: Unified Space-time Video Inpainting via Mixture-of-Experts
Zhen Wan, Chenyang Qi, Zhiheng Liu +2
In this paper, we present UniPaint, a unified generative space-time video inpainting framework that enables spatial-temporal inpainting and interpolation. Different from existing m…
On Bott--Samelson rings for Coxeter groups
Tao Gui, Lin Sun, Shihao Wang +1
We study the cohomology ring of the Bott--Samelson variety. We compute an explicit presentation of this ring via Soergel's result, which implies that it is a purely combinatorial i…
Equivariant log-concavity and equivariant Kähler packages
Tao Gui, Rui Xiong
We show that the exterior algebra , which is the cohomology of the torus , and the polynomial ring $\mathbb{R}\left[t_{1},…