Let(W,S) be a Coxeter group with S = I■J such that J consists of all universal elements of S and that I generates a finite parabolic subgroup W_I of W with w_0 the longest element of W_I. We describe all the left cel...Let(W,S) be a Coxeter group with S = I■J such that J consists of all universal elements of S and that I generates a finite parabolic subgroup W_I of W with w_0 the longest element of W_I. We describe all the left cells and two-sided cells of the weighted Coxeter group(W,S,L) that have non-empty intersection with W_J,where the weight function L of(W, S) is in one of the following cases:(i) max{L(s) | s ∈J} < min{L(t)|t∈I};(ii) min{L(s)|s ∈J} ≥L(w_0);(iii) there exists some t ∈ I satisfying L(t) < L(s) for any s ∈I-{t} and L takes a constant value L_J on J with L_J in some subintervals of [1, L(w_0)-1]. The results in the case(iii) are obtained under a certain assumption on(W, W_I).展开更多
We define and study cocycles on a Coxeter group in each degree generalizing the sign function.When the Coxeter group is a Weyl group,we explain how the degree three cocycle arises naturally from geometric representati...We define and study cocycles on a Coxeter group in each degree generalizing the sign function.When the Coxeter group is a Weyl group,we explain how the degree three cocycle arises naturally from geometric representation theory.展开更多
Let w be the element of maximal length in a finite irreducible Coxeter system （W, S）. In the present paper, we get the length of w when （W, S） is of type An, Bn/Cn or Dn.
The concept of norm and cellular algebra are introduced and then the cellular basis is used to replace the Kazhdan-Lusztig basis. So a new base for the center of generic Hecke algebra associated with finite Coxeter gr...The concept of norm and cellular algebra are introduced and then the cellular basis is used to replace the Kazhdan-Lusztig basis. So a new base for the center of generic Hecke algebra associated with finite Coxeter group is found. The new base is described by using the notion of cell datum of Graham and Lehrer and the notion of norm.展开更多
We introduce the mutation game on a directed multigraph,which is dual to Mozes5 numbers game.This new game allows us to create geometric and combinatorial structure that allows generalization of root systems to more g...We introduce the mutation game on a directed multigraph,which is dual to Mozes5 numbers game.This new game allows us to create geometric and combinatorial structure that allows generalization of root systems to more general graphs.We interpret Coxeter-Dynkin diagrams in this multigraph context and exhibit new geometric forms for the associated root systems.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11131001 and 11471115)Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeScience and Technology Commission of Shanghai Municipality (Grant No.13dz2260400)
文摘Let(W,S) be a Coxeter group with S = I■J such that J consists of all universal elements of S and that I generates a finite parabolic subgroup W_I of W with w_0 the longest element of W_I. We describe all the left cells and two-sided cells of the weighted Coxeter group(W,S,L) that have non-empty intersection with W_J,where the weight function L of(W, S) is in one of the following cases:(i) max{L(s) | s ∈J} < min{L(t)|t∈I};(ii) min{L(s)|s ∈J} ≥L(w_0);(iii) there exists some t ∈ I satisfying L(t) < L(s) for any s ∈I-{t} and L takes a constant value L_J on J with L_J in some subintervals of [1, L(w_0)-1]. The results in the case(iii) are obtained under a certain assumption on(W, W_I).
文摘We define and study cocycles on a Coxeter group in each degree generalizing the sign function.When the Coxeter group is a Weyl group,we explain how the degree three cocycle arises naturally from geometric representation theory.
文摘Let w be the element of maximal length in a finite irreducible Coxeter system （W, S）. In the present paper, we get the length of w when （W, S） is of type An, Bn/Cn or Dn.
文摘The concept of norm and cellular algebra are introduced and then the cellular basis is used to replace the Kazhdan-Lusztig basis. So a new base for the center of generic Hecke algebra associated with finite Coxeter group is found. The new base is described by using the notion of cell datum of Graham and Lehrer and the notion of norm.
文摘We introduce the mutation game on a directed multigraph,which is dual to Mozes5 numbers game.This new game allows us to create geometric and combinatorial structure that allows generalization of root systems to more general graphs.We interpret Coxeter-Dynkin diagrams in this multigraph context and exhibit new geometric forms for the associated root systems.
基金supported by National Natural Science Foundation of China(Grant No. 10731070)the Doctoral Program of Higher Educationthe Fundamental Research Funds for the Central University
文摘In the present paper we determine the representation type of the 0-Hecke algebra of a finite Coxeter group.
