6 citations · 16 across the 7 of their papers we have counts for
7 papers
Gelfand-Kirillov dimensions and associated varieties of highest weight modules
Zhanqiang Bai, Wei Xiao, Xun Xie
In this paper, we present a uniform formula of Lusztig's -functions on classical Weyl groups. Then we obtain an efficient algorithm for the Gelfand-Kirillov dimensions…
Associated varieties of minimal highest weight modules
Zhanqiang Bai, Jia-Jun Ma, Wei Xiao +1
Let be a complex simple Lie algebra. A simple -module is called minimal if the associated variety of its annihilator ideal coincides with the closure o…
Conjectures P1-P15 for hyperbolic Coxeter groups of rank 3
Jianwei Gao, Xun Xie
We prove Lusztig's conjectures P1-P15 for hyperbolic Coxeter groups of rank 3. Our proof enables us to give a description of the a-function and Kazhdan-Lusztig cells for these Coxe…
Conjectures P1-P15 for Coxeter groups with complete graph
Xun Xie
We prove Lusztig's conjectures P1-P15 for Coxeter groups with complete graph, using deceasing induction on -values and a kind of decomposition formula of Kazhdan-Lusz…
Gelfand-Kirillov Dimensions of Highest Weight Harish-Chandra Modules for
Zhanqiang Bai, Xun Xie
Let be an irreducible Hermitian symmetric pair of non-compact type with , and let be an integral weight such that the simple highest weight module $ L(λ)…
A decomposition formula for the Kazhdan-Lusztig basis of affine Hecke algebras of rank 2
Xun Xie
In this paper, we prove a decomposition formula for the Kazhdan-Lusztig basis of affine Hecke algebras of rank 2 with positive weight function. Then we discuss some applications of…
The based ring the lowest generalized two-sided cell of an extended affine Weyl group
Xun Xie
Let be the lowest generalized two-sided cell of an extended affine Weyl group W. We determine the structure of the based ring of . For this we show tha…