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Non-vanishing of Single, Double, and Triple Schubert Structure Constants
Yiming Chen, Neil J. Y. Fan, Rui Xiong +1
The Schubert vanishing problem asks whether the single Schubert coefficients are zero. In this paper, we consider the non-vanishing problems of double Schubert coeffici…
Quantized Coulomb Branches of Separated Cotangent Type and Orthosymplectic Quivers
Yaolong Shen, Changjian Su, Rui Xiong
We propose a definition of the quantized Coulomb branches of separated cotangent type, and prove that the corresponding classical construction recovers the non-cotangent Coulomb br…
A solution to Butler's positivity conjecture
Peter L. Guo, Mingyang Kang, Rui Xiong
Let be distinct partitions such that and . We prove Butler's positivity conjecture posed in 1994: the expansion of the Macdonald intersecti…
On weight modules over truncated shifted iYangians
Yaolong Shen, Linliang Song, Rui Xiong
Truncated shifted iYangians are a family of algebras expected to quantize certain components of affine Grassmannian islices. We introduce orientifold KLRW (oKLRW) algebras associat…
Equivariant Schubert Calculus for Inverse Grassmannian Permutations
Yiming Chen, Neil J. Y. Fan, Rui Xiong +1
We give a Graham-positive expansion for the product of two double Schubert polynomials indexed by two inverse Grassmannian permutations. Surprisingly, the nonzero structure constan…
Motivic Chern Classes of Open Projected Richardson Varieties and of Affine Schubert Cells
Changjian Su, Rui Xiong, Changlong Zhong
The open projected Richardson varieties are images of the open Richardson varieties of the complete flag variety under the canonical projection to the partial flag variety. Our mai…