Related papers: A Generalization of an Alternating Sum Formula for…

For any Coxeter system $(W,S)$ of rank $n$, we introduce an abstract boolean complex (simplicial poset) of dimension $2n-1$ that contains the Coxeter complex as a relative subcomplex. Faces are indexed by triples $(I,w,J)$, where $I$ and…

The descent algebra of a finite Coxeter group $W$ is a basic algebra, and as such it has a presentation as quiver with relations. In recent work, we have developed a combinatorial framework which allows us to systematically compute such a…

We obtain the equivariant K-homology of the classifying space \underline{E}W for W a right-angled or, more generally, an even Coxeter group. The key result is a formula for the relative Bredon homology of \underline{E}W in terms of Coxeter…

The OGS for non-abelian groups is an interesting generalization of the basis of finite abelian groups. The definition of OGS states that every element of a group has a unique presentation as a product of some powers of specific generators…

Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper we prove a family of identities involving Bernoulli numbers and apply them to obtain…

A new general formula for the number of conjugacy classes of subgroups of given index in a finitely generated group is obtained.

We use the theory of symmetric functions to enumerate various classes of alternating permutations w of {1,2,...,n}. These classes include the following: (1) both w and w^{-1} are alternating, (2) w has certain special shapes, such as…

A Coxeter system is an ordered pair (W,S) where S is the generating set in a particular type of presentation for the Coxeter group W. A subgroup of W is called special if it is generated by a subset of S. Amalgamated product decompositions…

We determine a fundamental domain for the diagonal action of a finite Coxeter group $W$ on $V^{\oplus n}$, where $V$ is the reflection representation. This is used to give a stratification of $V^{\oplus n}$, which is respected by the group…

The G-function associated to the semi-simple Frobenius manifold C^n/W (where W is a Coxeter group or an extended affine Weyl group) is studied. The general form of the G function is given in terms of a logarithmic singularity over caustics…

Let W be a finite group generated by unitary reflections and A be the set of reflecting hyperplanes. We will give a characterization of the logarithmic differential forms with poles along A in terms of anti-invariant differential forms. If…

Let $\mathcal{H}$ be a Coxeter hyperplane arrangement in $n$-dimensional Euclidean space. Assume that the negative of the identity map belongs to the associated Coxeter group $W$. Furthermore assume that the arrangement is not of type…

We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both…

In this article we prove an algebraic identity which significantly generalizes the formula for sum of powers of consecutive integers involving Stirling numbers of the second kind. Also we have obtained a generalization of Newton-Girard…

Artin groups are a natural generalization of braid groups and are well-understood in certain cases. Artin groups are closely related to Coxeter groups. There is a faithful representation of a Coxeter group $W$ as a linear reflection group…

By Theorem~1.12 of the paper "A Class of Representations of Hecke Algebras", if $W$ is a Coxeter group whose proper parabolic subgroups are finite, and if the module of a finite $W$-digraph $\Gamma$ is isomorphic to the module of a…

Let $W$ be a finite Coxeter group and $X$ a subset of $W$. The length polynomial $L_{W,X}(t)$ is defined by $L_{W,X}(t) = \sum_{x \in X} t^{\ell(x)}$, where $\ell$ is the length function on $W$. In this article we derive expressions for the…

Let $G$ be a simple algebraic group over an algebraically closed field $\mathbb{F}$ of characteristic $p\geq h$, the Coxeter number of $G$. We observe an easy `recursion formula' for computing the Jantzen sum formula of a Weyl module with…

A family of polynomials parameterized by the conjugacy classes of a finite Coxeter group is investigated. These polynomials, together with the character table of the group, determine the associated generic degrees. The polynomials are…

The descent algebra $\Sigma(W)$ is a subalgebra of the group algebra $\Q W$ of a finite Coxeter group $W$, which supports a homomorphism with nilpotent kernel and commutative image in the character ring of $W$. Thus $\Sigma(W)$ is a basic…