Related papers: On Gelfand models for finite Coxeter groups

Let $G$ be a discrete group. We prove that the category of $G$-posets admits a model structure that is Quillen equivalent to the standard model structure on $G$-spaces. As is already true nonequivariantly, the three classes of maps defining…

Let ${\mathbb{F}_{q}}$ be the finite field of order $q$. Let $G$ be one of the three groups ${\rm GL}(n, \mathbb{F}_q)$, ${\rm SL}(n, \mathbb{F}_q)$ or ${\rm U}(n, \mathbb{F}_q)$ and let $W$ be the standard $n$-dimensional representation of…

In this third part, we make the following hypothesis: representation $R=R(\alpha,\beta,\gamma ;l)$ of $W(p,q,r)$ is reducible and there exist a $G$-invariant non-nulle bilinear form where $G=Im R$. With those conditions, we know the…

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…

In this fourth part, (with the notations of the preceding parts) we make the following hypothesis: $(W,S)$ is a Coxeter system, irreducible, $2$-spherical and $S$ is finite. Let $R:W\to GL(M)$ be a reducible reflection representation of…

For $G$ a finite group, we show that functions on fields for the 2-dimensional supersymmetric sigma model with background $G$-symmetry determine cocycles for complex analytic $G$-equivariant elliptic cohomology. Similar structures in…

Let $\mathfrak{o}$ be the ring of integers of a non-archimedean local field with the maximal ideal $\wp$ and the finite residue field of characteristic $p.$ Let $\mathbf{G}$ be the General Linear or Special Linear group with entries from…

We develop a framework to construct geometric representations of finite groups $G$ through the correspondence between real toric spaces $X^{\mathbb R}$ and simplicial complexes with characteristic matrices. We give a combinatorial…

This paper and its sequel describe the irreducible representations of the rational Cherednik algebra $H_c(W)$ for a finite Coxeter group $W$ of type $H_4$, $F_4$ with equal parameters, $E_6$, $E_7$, and $E_8$, when $c$ is not a…

We study the (complex) Hecke algebra $\mathcal{H}_S(\mathbf{q})$ of a finite simply-laced Coxeter system $(W,S)$ with independent parameters $\mathbf{q} \in \left( \mathbb{C} \setminus\{\text{roots of unity}\} \right)^S$. We construct its…

Given a subgroup H of a finite group G, we begin a systematic study of the partial representations of G that restrict to global representations of H. After adapting several results from [DEP00] (which correspond to the case where H is…

We provide a new tableau model from which one can easily deduce the characters of finite-dimensional irreducible polynomial representations of the special orthogonal group $SO_n(\mathbb{C})$. This model originates from the representation…

For an arbitrary finite monoid $M$ and subgroup $K$ of the unit group of $M$, we prove that there is a bijection between irreducible representations of $M$ with nontrivial $K$-fixed space and irreducible representations of $\mathcal{H}_K$,…

In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…

Aiming for a revival of the theory of crystallographic complex reflection groups, we compute (minimal) Coxeter-like reflection presentations for the infinite families of those non-genuine groups which satisfy Steinberg's fixed point…

We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted…

The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. Using the result we establish a one to one correspondence between the set of…

Let $G$ be a connected, reductive group over a non-archimedean local field $F$. Let $\breve F$ be the completion of the maximal unramified extension of $F$ contained in a separable closure $F_s$. In this article, we construct a Tits group…

We adapt methods from quiver representation theory and Hall algebra techniques to the counting of representations of virtually free groups over finite fields. This gives rise to the computation of the E-polynomials of…

Given a finite group $G,$ we denote by $\Delta(G)$ the graph whose vertices are the proper subgroups of $G$ and in which two vertices $H$ and $K$ are joined by an edge if and only if $G=\langle H,K\rangle.$ We prove that if there exists a…