相关论文: Invariant functions on symplectic representations

We study quantum moment maps of $G$-invariant star products, which are a quantum analogue of the moment map for classical Hamiltonian systems. Introducing an integral representation, we show that any quantum moment map for a $G$-invariant…

The quantum analogue of general relativistic geometry should be implementable on smooth manifolds without an a priori metric structure, the kinematical covariance group acting by diffeomorphisms. Here I approach quantum gravity (QG) in the…

Assume $(X, \omega)$ is a compact symplectic manifold with a Hamiltonian compact Lie group action and the zero in the Lie algebra is a regular value of the moment map $\mu$. We prove that a finite energy symplectic vortex exponentially…

A generalized semitoric system F:=(J,H): M --> R^2 on a symplectic 4-manifold is an integrable system whose essential properties are that F is a proper map, its set of regular values is connected, J generates an S^1-action and is not…

Let $A$ be an abelian variety and $G$ a finite group of automorphisms of $A$ fixing the origin such that $A/G$ is smooth. The quotient $A/G$ can be seen as a fibration over an abelian variety whose fibers are isomorphic to a product of…

Given a finite p-group G acting on a smooth projective curve X over an algebraically closed field k of characteristic p, the dimension of the tangent space of the associated equivariant deformation functor is equal to the dimension of the…

In this note we introduce parameterized Gromov-Witten invariants for symplectic fiber bundles and study the topology of the symplectomorphism group. We also give sample applications showing the non-triviality of certain homotopy groups of…

Let $G$ be an algebraic group and let $X$ be a smooth $G$-variety with two orbits: an open orbit and a a closed orbit of codimension $1$. We give an algebraic description of the category of $G$-equivariant vector bundles on $X$ under a mild…

We construct a quadratic Morse-Bott function on the real Grassmannian of a symplectic vector space from a compatible linear complex structure. We show that its critical loci consist of linear subspaces that split into isotropic and complex…

The paper presents a new algorithmic construction of a finite generating set of rational invariants for the rational action of an algebraic group on the affine space. The construction provides an algebraic counterpart of the moving frame…

Quiver varieties have recently appeared in various different areas of Mathematics such as representation theory of Kac-Moody algebras and quantum groups, instantons on 4-manifolds, and resolutions Kleinian singularities. In this paper, we…

We study the cohomological properties of the fixed locus $X^G$ of an automorphism group $G$ of prime order $p$ acting on a variety $X$ whose integral cohomology is torsion-free. We obtain an precise relation between the mod $p$ cohomology…

We compare the K-theories of symplectic quotients with respect to a compact connected Lie group and with respect to its maximal torus, and in particular we give a method for computing the former in terms of the latter. More specifically,…

Let G denote either a special orthogonal group or a symplectic group defined over the complex numbers. We prove the following saturation result for G: given dominant weights \lambda^1, ..., \lambda^r such that the tensor product…

We give an answer to the abstract Capelli problem: Let $(G, V)$ be a multiplicity-free finite-dimensional representation of a connected reductive complex Lie group $G$ and $G'$ be its derived subgroup. Assume that the categorical quotient…

A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck's Quot scheme. Over nodal curves, a relative construction is made to keep the torsion…

We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions which was recently studied as a vector space by Rosas and Sagan. The bases for this algebra are indexed by set partitions. We show that there…

We present a generalized version of classical geometric invariant theory \`a la Mumford where we consider an affine algebraic group $G$ acting on a specific affine algebraic variety $X$. We define the notions of linearly reductive and of…

We introduce geometric quantization for constant rank presymplectic structures with Riemannian null foliation and compact leaf closure space. We prove a quantization-commutes-with-reduction theorem in this context. Examples related to…

We show that every involutive Hopf monoid in a complete and finitely cocomplete symmetric monoidal category gives rise to invariants of oriented surfaces defined in terms of ribbon graphs. For every ribbon graph this yields an object in the…