2 citations · 7 across the 18 of their papers we have counts for
18 papers
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…
Combinatorial Aspects of Elliptic Schubert Calculus
Cristian Lenart, Rui Xiong, Changlong Zhong
The main goal of this paper is to extend two fundamental combinatorial results in Schubert calculus on flag manifolds from equivariant cohomology and -theory to equivariant elli…
Hybrid Pipe Dreams for Key Polynomials
Yihan Xiao, Rui Xiong, Haofeng Zhang
We develop a family of new combinatorial models for key polynomials. It is similar to the hybrid pipe dream model for Schubert polynomials defined recently by Knutson and Udell.
Automorphisms of the Quantum Cohomology of the Springer Resolution and Applications
Changzheng Li, Changjian Su, Rui Xiong
In this paper, we introduce quantum Demazure--Lusztig operators acting by ring automorphisms on the equivariant quantum cohomology of the Springer resolution. Our main application…
Structure algebras, Hopf algebroids and oriented cohomology of a group
Martina Lanini, Rui Xiong, Kirill Zainoulline
We prove that the structure algebra of a Bruhat moment graph of a finite real root system is a Hopf algebroid with respect to the Hecke and the Weyl actions. We introduce new techn…
Pieri and Murnaghan--Nakayama type Rules for Chern classes of Schubert Cells
Neil J. Y. Fan, Peter L. Guo, Rui Xiong
We develop Pieri type as well as Murnaghan--Nakayama type formulas for equivariant Chern--Schwartz--MacPherson classes of Schubert cells in the classical flag variety. These formul…
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…
A Geometric Realization of Symmetric Pairs of Type AIII
Rui Xiong
In this paper, we construct a geometric realization of symmetric pair of type AIII over -quiver varieties as an analogy of the construction over Nakajima quiver varieties. To ac…
Cauchy Formulas and Billey's Formulas for Generalized Grothendieck polynomials
Rui Xiong
We study the generalized double -Grothendieck polynomials for all types. We study the Cauchy formulas for them. Using this, we deduce the K-theoretic version of the comodule str…
Computations of the Comodule Structures of the Chow rings of Flag Varieties
Rui Xiong
Let be a connected reductive group, and be its flag variety. Let be the natural projection. In this paper, we developed an algorithm to describe the map $π^*…
Puzzle Model for Bumpless Pipe Dream
Rui Xiong
In this note, a new puzzle is introduced where the pipe dream and bumpless pipe dream can be played simultaneously. Using these, a combinatorial proof of the (ordinary) Schubert po…
Comodule Structures, Equivariant Hopf Structures, and Generalized Schubert Polynomials
Rui Xiong
In this article, the comodule structure of Chow rings of Flag manifolds is described by Schubert cells. Its equivariant version gives rise to a Hopf struct…
A bijection proof of the Capelli's identity
Rui Xiong
In this article, a short combinatorial proof of the Capelli's identity is given. It also leads to an easy proof of the Capelli--Cauchy--Binet identity, a more general form of Capel…
Schur Polynomials through Lindström Gessel Viennot Lemma
Rui Xiong
In this article, we use Lindström Gessel Viennot Lemma to give a short, combinatorial, visualizable proof of the identity of Schur polynomials -- the sum of monomials of Young tabl…
Kernel-Cokernel Sequence for Composition and its Applications
Rui Xiong
If this article, an elementary kernel-cokernel exact sequence is introduced for . Some relative sequences and applications are dicussed. This r…
A short proof of Spectral Sequences of Filtered Complexes
Rui Xiong
The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cl…
Direct proof of Mckay Correspondence and the representations of finite subgroups of
Rui Xiong
The classic Mckay correspondence gives a connection between finite subgroups of and the simply-laced Dynkin diagrams. In this article, a direct proof is pres…
On the structure of submodule of finitely generated module over PID
Rui Xiong
Consider , and the subgroup generated by , it is a subgroup isomorphic to . If my theorem holds,…