Hongsheng Hu

collaborators

4 papers

math.CO2025

Asymptotic Log-concavity of Dominant Lower Bruhat Intervals via Brunn--Minkowski Inequality

Gaston Burrull, Tao Gui, Hongsheng Hu

BjÃ¶rner 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 crystallogr…

math.AT2025

Weyl group symmetries of the toric variety associated with Weyl chambers

Tao Gui, Hongsheng Hu, Minhua Liu

For any crystallographic root system, let $W$ be the associated Weyl group, and let $WP$ be the weight polytope (also known as the $W$ -permutohedron) associated with an ar…

math.RT2025

On exterior powers of reflection representations, II

Hongsheng Hu

Let $W$ be a group endowed with a finite set $S$ of generators. A representation $(V, I ¨ )$ of $W$ is called a reflection representation of $(W, S)$ if $I ¨ (s)$ is a (generalized) refl…

math.RT2024

Strongly dominant weight polytopes are cubes

Gaston Burrull, Tao Gui, Hongsheng Hu

For any root system of rank $r$ , we study the "dominant weight polytope" $P^{I^} »$ associated with a strongly dominant weight $I^»$ . We prove that $P^{I^} »$ is combinatorially equivalent…