2 citations · 2 across the 7 of their papers we have counts for
9 papers
Lattice Bruhat intervals are polytopal
Yibo Gao, Tao Gui
For a Bruhat interval in an arbitrary Coxeter group which is a lattice, we give a type-uniform construction of a convex polytope whose complete face lattice realizes $[x,y]…
Equivariant multiplicities and torsion at attractive fixed points
Tao Gui, Peter L. Guo, Zhuowei Lin
Let \(X\) be a rationally smooth complex affine variety with a torus action and an attractive fixed point \(x\). Suppose that \(X\setminus\{x\}\) is \(p\)-smooth and that its integ…
Permutation Representations on Cohomology of Toric Varieties
Tao Gui, Chushi Qin, Kaizhe Shen +1
Let be a finite group acting properly by lattice automorphisms on a complete simplicial fan . An open question due to Stanley asked whether the (ungraded) representation car…
Complete simplicial fans, Stanley--Reisner rings, and equivariant h-polynomials
Tao Gui
We derive a graded character formula for the action of any finite group on the Artinian reduction of the Stanley--Reisner ring of any complete simplicial fan, which is given by an…
Weyl group symmetries of the toric variety associated with Weyl chambers
Tao Gui, Hongsheng Hu, Minhua Liu
For any crystallographic root system, let be the associated Weyl group, and let be the weight polytope (also known as the -permutohedron) associated with an ar…
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…
Asymptotic Log-concavity of Dominant Lower Bruhat Intervals via Brunn--Minkowski Inequality
Gaston Burrull, Tao Gui, Hongsheng Hu
Björner and Ekedahl [Ann. of Math. (2), 170.2(2009), pp. 799--817] pioneered the study of length-counting sequences associated with parabolic lower Bruhat intervals in crystallogra…
Strongly dominant weight polytopes are cubes
Gaston Burrull, Tao Gui, Hongsheng Hu
For any root system of rank , we study the "dominant weight polytope" associated with a strongly dominant weight . We prove that is combinatorially equivalent to…
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}, \l…