Related papers: Higher signs for Coxeter groups
This paper constructs a representation of a Hecke algebra on a vector space spanned by the involutions in a Coxeter group.
We use geometry of Davis complex of a Coxeter group to prove the following result: if G is an infinite indecomposable Coxeter group and $H\subset G$ is a finite index reflection subgroup then the rank of H is not less than the rank of G.…
In this short note we discuss the interplay between finite Coxeter groups and construction of wavelet sets, generalized multiresolution analysis and sampling.
A representation theory for Bol algebras is proposed. For a suitable (2,3)-cohomology theory for Bol algebras, we define a (2,3)-coboundary with companion and next we define a (2,3)-cohomology group. Deformations of Bol algebras are…
For a finite Coxeter system and a subset of its diagram nodes, we define spherical elements (a generalization of Coxeter elements). Conjecturally, for Weyl groups, spherical elements index Schubert varieties in a flag manifold G/B that are…
We investigate the study of smooth irreducible rational curves in $Y_s^r$, a general blowup of $\mathbb{P}^r$ at $s$ general points, whose normal bundle splits as a direct sum of line bundles all of degree $i$, for $i \in \{-1,0,1\}$: we…
We introduce a notion of representation for a class of generalised quivers known as Coxeter quivers. These representations are built using fusion categories associated to $U_q(\mathfrak{s}\mathfrak{l}_2)$ at roots of unity and we show that…
A conjecture proposed by Gaetz and Gao asserts that the Cayley graph of any Coxeter group satisfies the strong hull property. In this paper, we prove this conjecture for all affine irreducible Coxeter groups of rank 3. Our approach exploits…
In this work we characterise Cayley graphs of Coxeter groups with respect to the standard generating set that admit uncountable vertex stabilisers. As a corollary, we fully identify finitely generated Coxeter groups for which the…
We study a class of algebraic surfaces of degree 3n in the complex projective space with only ordinary double points. They are obtained by using bivariate polynomials with complex coefficients related to the generalized cosine associated to…
We refine Brink's theorem, that the non-reflection part of a reflection centralizer in a Coxeter group W is a free group. We give an explicit set of generators for centralizer, which is finitely generated when W is. And we give a method for…
In this sixth part we study rank $3$ reflection groups not well generated: $G(2r,r,2)$, $G_{12}$, $G_{13}$ and $G_{22}$. We start from a reflection representation of a rank $3$ Coxeter group and we show that we can obtain in this manner…
The article investigates high-level general invertible-sequential processing in the digital and quantum domains. In particular it is shown that (i) invertible digital-sequential processes, constructed using a standard general-inversion…
This paper presents a natural generalisation of Saxl conjecture from a Lie-theoretical perspective, which is verified for the exceptional types. For classical types, progress is made using spin representations, revealing connections to…
We give an explicit formula for the signature of handlebody bundles over the circle in terms of the homological monodromy. This gives a cobounding function of Meyer's signature cocycle on the mapping class group of a $3$-dimensional…
Higher order group cohomology is defined and first properties are given. Using modular symbols, an Eichler-Shimura homomorphism is constructed mapping spaces of higher order cusp forms to higher order cohomology groups.
In this paper, we analyze the faithful representations of the dihedral groups, and prove that the Coxeter groups can be determined by the proper joint spectrum of their faithful representations.
We introduce a cohomology set for groups defined by algebraic difference equations and show that it classifies torsors under the group action. This allows us to compute all torsors for large classes of groups. We also develop some tools for…
The lower central series of the rgiht-angled Coxeter group $RC_\mathcal K$ and the corresponding graded Lie algebra $L(RC_\mathcal K)$ associated with the lower central series of a right-angled Coxeter group are studied. Relations are…
This is an extended and corrected version of the author's Diplomarbeit. A class of algebras called generic pro-$p$ Hecke algebras is introduced, enlarging the class of generic Hecke algebras by considering certain extensions of (extended)…