For any Coxeter group W, we define a filtration of H^*(W;ZW) by W-submodules and then compute the associated graded terms. More generally, if U is a CW complex on which W acts as a reflection group we compute the associated graded terms for H_*(U) and, in the case where the action is proper and cocompact, for H^*_c(U).
We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group $W$. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit basis of the space of $W$-invariants in this cohomology ring.
We study the subregular $J$-ring $J_C$ of a Coxeter system $(W,S)$, a subring of Lusztig's $J$-ring. We prove that $J_C$ is isomorphic to a quotient of the path algebra of the double quiver of $(W,S)$ by a suitable ideal that we associate to a family of Chebyshev polynomials. As applications, we use quiver representations to study the category mod-$A_K$ of finite dimensional right modules of the algebra $A_K=K\otimes_\Z J_C$ over an algebraically closed field $K$ of characteristic zero. Our results include classifications of Coxeter systems for which mod-$A_K$ is semisimple, has finitely many …
Poincare series of Klein groups, Coxeter polynomials, the Burau representation and Milnor invariants
对于二元多面体群的Poincare级数和Coxeter多项式，得到了与Euclid算法和正交多项式理论相近的命题：广义Ebeling公式，分解成分歧的连分数，Christoffel-Darboux恒等式，组合公式.关于亚历山大-康威多项式的因式分解的已知结果允许将庞加莱级数和考克斯特多项式与弦链的Burau表示和Milnor不变量连接起来。一个使用A 'Campo链路和Coxeter链路的重构。利用S. M. Gusein-Zade，F. Delgado和A.坎皮罗
The Hochschild cohomology rings for self-injective algebras of tree classes $E_7$ and $E_8$ with finite representation type was described in terms of generators and relations.
