Related papers: On quasiinvariants of $S_n$ of hook shape

In 2002, Feigin and Veselov defined the space of m-quasiinvariants for any Coxeter group, building on earlier work of Chalykh and Veselov. While many properties of those spaces were proven from this definition, an explicit computation of a…

The paper an elementary introduction for non-specialists to the theory of quasi-invariants of Coxeter groups. The main object of study is the variety X_m of quasi-invariants for a finite Coxeter group, which arose in a work of O.Chalykh and…

A basis of quasi-invariant module over invariants is explicitly constructed for the two-dimensional Coxeter systems with arbitrary multiplicities. It is proved that this basis consists of $m$-harmonic polynomials, thus the earlier results…

Let W be a finite Coxeter group in a Euclidean vector space V, and m a W-invariant Z_+-valued function on the set of reflections in W. Chalyh and Veselov introduced in an interesting algebra Q_m, called the algebra of m-quasiinvariants for…

The spaces of quasi-invariant polynomials were introduced by Chalykh and Veselov [Comm. Math. Phys. 126 (1990), 597-611]. Their Hilbert series over fields of characteristic 0 were computed by Feigin and Veselov [Int. Math. Res. Not. 2002…

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we…

Building upon work of Y. Shalom we give a homological-algebra flavored definition of an induction map in group homology associated to a topological coupling. As an application we obtain estimates of the (co)homological dimension of groups G…

Kashaev and Reshetikhin proposed a generalization of the Reshetikhin-Turaev link invariant construction to tangles with a flat connection in a principal G-bundle over the complement of the tangle. The purpose of this paper is to adapt and…

In the setting of geometric quantization, we associate to any prequantum bundle automorphism a unitary map of the corresponding quantum space. These maps are controlled in the semiclassical limit by two invariants of symplectic topology:…

Given a quasi-split reductive group $G$ and a symmetric variety $X$, we introduce a notion of endoscopic varieties for $(G,X)$, and establish the foundational properties of these varieties such as matching of stable semi-simple orbits. To…

The rings of quantum integrals of the generalized Calogero-Moser systems related to the deformed root systems ${\cal A}_n(m)$ and ${\cal C}_n(m,l)$ with integer multiplicities and corresponding algebras of quasi-invariants are investigated.…

In this paper, we give two elementary constructions of homogeneous quasi-morphisms defined on the group of Hamiltonian diffeomorphisms of certain closed connected symplectic manifolds (or on its universal cover). The first quasi-morphism,…

Double (quasi-)Poisson brackets were introduced on associative algebras by Van den Bergh to induce a (quasi-)Poisson structure on their representation spaces naturally equipped with a $\mathrm{GL}$-action (type $\mathtt{A}$). If there…

We introduce the notion of a relative spherical category. We prove that such a category gives rise to the generalized Kashaev and Turaev-Viro-type 3-manifold invariants defined in arXiv:1008.3103 and arXiv:0910.1624, respectively. In this…

We introduce quasi-invariant polynomials for an arbitrary finite complex reflection group W. Unlike in the Coxeter case, the space Q_k of quasi-invariants of a given multiplicity is not, in general, an algebra but a module over the…

Suppose V is a finite dimensional, complex vector space, A is a finite set of codimension one subspaces of V, and G is a finite subgroup of the general linear group GL(V) that permutes the hyperplanes in A. In this paper we study invariants…

We prove that the cohomology of semi-simple Lie groups admits boundary values, which are measurable cocycles on the Furstenberg boundary. This generalises known invariants such as the Maslov index on Shilov boundaries, the Euler class on…

The author, and independently De Concini, conjectured that the monodromy of the Casimir connection of a simple Lie algebra g is described by the quantum Weyl group operators of the quantum group U_h(g). The aim of this paper, and of its…

A strong version of the quantization conjecture of Guillemin and Sternberg is proved. For a reductive group action on a smooth, compact, polarized variety (X,L), the cohomologies of L over the GIT quotient X // G equal the invariant part of…

We classify insulators by generalized symmetries that combine space-time transformations with quasimomentum translations. Our group-cohomological classification generalizes the nonsymmorphic space groups, which extend point groups by…