Related papers: Refined Gelfand models for wreath products
This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of Eilenberg-Moore algebras of involutive…
The Gelfand representation of $\mathcal{S}_n$ is the multiplicity-free direct sum of the irreducible representations of $\mathcal{S}_n$. In this paper, we use a result of Adin, Postnikov, and Roichman to find a recursive generating function…
It is known that the notion of a transitive subgroup of a permutation group $P$ extends naturally to the subsets of $P$. We study transitive subsets of the wreath product $G \wr S_n$, where $G$ is a finite abelian group. This includes the…
In this article, we present a combinatorial formula for computing the Wedderburn decomposition of the rational group algebra associated with an ordinary metacyclic $p$-group $G$, where $p$ is any prime. We also provide a formula for…
We consider the finitely generated groups acting on a regular tree with almost prescribed local action. We show that these groups embed as cocompact irreducible lattices in some locally compact wreath products. This provides examples of…
In Finite Group Modular Representation Theory, the basic objects are the indecomposable and simple modules. This paper offers a new classification of these objects that refines the Green Theory Classification of indecomposable and simple…
After having established elementary results on the relationship between a finite complex (pseudo-)reflection group W < GL(V) and its reflection arrangement A, we prove that the action of W on A is canonically related with other natural…
We propose an analogue of Solomon's descent theory for the case of a wreath product G ~ S_n, where G is a finite abelian group. Our construction mixes a number of ingredients: Mantaci-Reutenauer algebras, Specht's theory for the…
Consider the generalized iterated wreath product $S_{r_1}\wr \ldots \wr S_{r_k}$ of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection…
We continue [GbSh:568] (math.LO/0003164), proving a stronger result under the special continuum hypothesis (CH). The original question of Eklof and Mekler related to dual abelian groups. We want to find a particular example of a dual group,…
We prove a decomposition theorem for irreducible components of Grassmannians of submodules, as well as for other schemes arising from representation theory, thus generalising the result of Crawley-Boevey and Schroer for module varieties.…
We show that the category of internal groupoids in an exact Mal'tsev category is reflective, and in fact a Birkhoff subcategory of the category of simplicial objects. We then characterize the central extensions of the corresponding Galois…
We provide simple presentations in terms of generators and relations for the invariant subring of both the Orlik--Solomon algebra and Varchenko--Gel'fand ring of the type $A_n$ reflection arrangement acted upon by the type $A_{n-1}$…
It is well known that there exist non-isomorphic compact groups with isomorphic representation rings (fusion rules). Nevertheless, considerable structural information about the group can be reconstructed from its representation ring. We…
We consider the complex reflection group \( \mathcal{G} \), identified as No. 8 in the Shephard-Todd classification. In this paper, we present computations of the vector-valued invariants associated with various representations of \(…
This is the fifth in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars.…
Schur modules give the irreducible polynomial representations of the general linear group $\mathrm{GL}_t$. Viewing the symmetric group $\mathfrak{S}_t$ as a subgroup of $\mathrm{GL}_t$, we may restrict Schur modules to $\mathfrak{S}_t$ and…
We obtain variational formulas for holomorphic objects on Riemann surfaces with respect to arbitrary local coordinates on the moduli space of complex structures. These formulas are written in terms of a canonical object on the moduli space…
Let A = (A,V) be a complex hyperplane arrangement and let L(A) denote its intersection lattice. The arrangement A is called supersolvable, provided its lattice L(A) is supersolvable, a notion due to Stanley. Jambu and Terao showed that…
We construct the Lafforgue variety, an affine scheme equipped with an open dense subscheme parametrizing the simple modules of a non-commutative unital algebra $R$ over any field $k$, provided that the center $Z(R)$ is finitely generated…