Related papers: McKay correspondence for symplectic quotient singu…

In this paper we prove the following results: $1)$ We show that any arithmetic quotient of a homogeneous space admits a natural real semi-algebraic structure for which its Hecke correspondences are semi-algebraic. A particularly important…

This thesis addresses questions in representation and invariant theory of finite groups. The first concerns singularities of quotient spaces under actions of finite groups. We introduce a class of finite groups such that the quotients have…

In this article we give formulas for the Riemann-Roch number of a symplectic quotient arising as the reduced space corresponding to a coadjoint orbit (for an orbit close to 0) as an evaluation of cohomology classes over the reduced space at…

We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, spaces of representations of quivers, and on…

Let G be a reductive linear algebraic group, H a reductive subgroup of G and X an affine G-variety. Let Y denote the set of fixed points of H in X, and N(H) the normalizer of H in G. In this paper we study the natural map from the quotient…

A reductive homogeneous space $G/H$ is always diffeomorphic to the normal bundle of an orbit of a maximal compact subgroup of $G$. We prove that if $G/H$ admits compact quotients, then the sphere bundle associated to this normal bundle is…

Let $G$ be a simple complex Lie group, $\alg{g}$ be its Lie algebra, $K$ be a maximal compact form of $G$ and $\alg{k}$ be a Lie algebra of $K$. We denote by $X\rightarrow \overline{X}$ the anti-involution of $\alg{g}$ which singles out the…

Let T be an algebraic torus acting on a smooth variety V. We study the relationship between the various GIT quotients of V and the symplectic quotient of the cotangent bundle of V.

Let $G$ denote a connected semisimple and simply connected algebraic group over an algebraically closed field $k$ of positive characteristic and let $g$ denote a regular element of $G$. Let $X$ denote any equivariant embedding of $G$. We…

We consider canonical symplectic structure on the moduli space of flat ${\g}$-connections on a Riemann surface of genus $g$ with $n$ marked points. For ${\g}$ being a semisimple Lie algebra we obtain an explicit efficient formula for this…

Given a linear action of a group $G$ on a $K$-vector space $V$, we consider the invariant ring $K[V \oplus V^*]^G$, where $V^*$ is the dual space. We are particularly interested in the case where $V =\gfq^n$ and $G$ is the group $U_n$ of…

Let $G = GL(V)$ for an N-dimensional vector space $V$ over an algebraically closed field k, and $G^{\theta}$ the fixed point subgroup of $G$ under an involution $\theta$ on $G$. In the case where $G^{\theta} = O(V)$, the generalized…

We describe the structure of the quotient $\mathfrak{G}/\mathfrak{H}$ of a formal supergroup $\mathfrak{G}$ by its formal sub-supergroup $\mathfrak{H}$. This is a consequence which arises as a continuation of the authors' work (partly with…

Let X=G/H be the quotient of a connected reductive algebraic C-group G defined over the field of complex numbers C by a finite subgroup H. We describe the topological fundamental group of the homogeneous space X, which is nonabelian when H…

We prove that the moduli space of gauge equivalence classes of symplectic vortices with uniformly bounded energy in a compact Hamiltonian manifold admits a Gromov compactification by polystable vortices. This extends results of Mundet i…

Let $G$ be a semisimple Lie group with finite component group, and let $K<G$ be a maximal compact subgroup. We obtain a quantisation commutes with reduction result for actions by $G$ on manifolds of the form $M = G\times_K N$, where $N$ is…

We adapt algorithms for resolving the singularities of complex algebraic varieties to prove that the natural map of homology theories from complex bordism to the bordism theory of complex derived orbifolds splits. In equivariant stable…

We study moduli spaces of flat connections on surfaces with boundary, with boundary conditions given by Lagrangian Lie subalgebras. The resulting symplectic manifolds are closely related with Poisson-Lie groups and their algebraic structure…

Let $G/P$ be a generalized flag variety, where $G$ is a complex semisimple connected Lie group and $P\subset G$ a parabolic subgroup. Let also $X\subset G/P$ be a Schubert variety. We consider the canonical embedding of $X$ into a…

Let $X$ be a simply connected rational elliptic space of formal dimension $n$ and let $\E(X)$ denote the group of homotopy classes of self-equivalences of $X$. If $X^{[k]}$ denotes the $k^{\text{th}}$ Postikov section of $X$ and $X^{k}$…