相关论文: Representations of wreath products on cohomology o…

In this paper, we study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. Our aim is to construct knot homologies categorifying…

We describe an algorithm for computing the complete set of primitive orthogonal idempotents in the centralizer ring of the permutation representation of a wreath product. This set of idempotents determines the decomposition of the…

We obtain new calculations of the top weight rational cohomology of the moduli spaces $\mathcal{M}_{2,n}$, equivalently the rational homology of the tropical moduli spaces $\Delta_{2,n}$, as a representation of $S_n$. These calculations are…

Procesi bundles are certain vector bundles on symplectic resolutions of symplectic quotient singularities for wreath-products of the symmetric groups with Kleinian groups. Roughly speaking, we can define Procesi bundles as bundles on…

Generalizing the centralizer construction of Molev and Olshanski on symmetric groups, we study the structures of the centralizer $\mZ_{m,n}$ of the wreath product $G_{n-m}$ in the group algebra of $G_n$ for any $n\geq m$. We establish the…

In \cite{CVX3}, we have established a Springer theory for the symmetric pair $(\operatorname{SL}(N),\operatorname{SO}(N))$. In this setting we obtain representations of (the Tits extension) of the braid group rather than just Weyl group…

The coefficients of the local $h$-polynomial of the barycentric subdivision of the simplex with $n$ vertices are known to count derangements in the symmetric group $\mathfrak{S}_n$ by the number of excedances. A generalization of this…

Let $G$ be a finite group, $X$ be a compact $G$-space. In this note we study the $(\mathbb{Z}_ + \times\mathbb{Z}/2\mathbb{Z})$-graded algebra $$\mathcal{F}^q_G(X) = \bigoplus_{n\geq0} q^n \cdot…

The Pieri rule gives an explicit formula for the decomposition of the tensor product of irreducible representation of the complex general linear group GL(n,C) with a symmetric power of the standard representation on C^n. It is an important…

We give a fully explicit description of Lie algebra derivatives (generalizing raising and lowering operators) for representations of SL(3,R) in terms of a basis of Wigner functions. This basis is natural from the point of view of principal…

We compute the rational Betti cohomology groups of the coarse moduli spaces of geometrically marked Del Pezzo surfaces of degree three and four as representations of the Weyl groups of the corresponding root systems. The proof uses a blend…

These lecture notes are based on lectures given by the author at the summer school "Arrangements in Pyr\'en\'ees" in June 2012. We survey and compare various compactifications of complex hyperplane arrangement complements. In particular, we…

Reidemeister (or twisted conjugacy) classes are considered in restricted wreath products of the form $G\wr \mathbb{Z}^k$, where $G$ is a finite group. For an automorphism $\varphi$ of finite order (supposed to be the same for the torsion…

Given a finite group $G$ acting on a set $X$ let $\delta_k(G,X)$ denote the proportion of elements in $G$ that have exactly $k$ fixed points in $X$. Let $\mathrm{S}_n$ denote the symmetric group acting on $[n]=\{1,2,\dots,n\}$. For…

We give a pedagogical survey of those aspects of the abstract representation theory of quantum groups which are related to the Tannaka-Krein reconstruction problem. We show that every concrete semisimple tensor *-category with conjugates is…

Let $U_\epsilon(\mathfrak g)$ be the simply connected quantized enveloping algebra associated to a finite-dimensional complex simple Lie algebra $\mathfrak g$ at the roots of unity. The De Concini-Kac-Procesi conjecture on the dimension of…

This is an extended abstract for a talk given at the mini-workshop "Cohomology rings and fundamental groups of hyperplane arrangements, wonderful compactifications, and real toric varieties", held in Oberwolfach, September 30-October 6,…

We give a geometric method for determining the cohomology groups and the product structure of a polyhedral product, under suitable freeness conditions or with coefficients taken in a field. This is done by considering first a special class…

Suppose $k$ is a finite field, that $C$ is a smooth projective geometrically irreducible curve over $k$, and that $n$ is a positive integer not divisible by the characteristic of $k$. In this paper we compute cup products of elements of the…

In this paper, we showed how a group acting regularly and a diagonal group are embedded into the wreath products in there product action using the Cartesian Decomposition.