Related papers: Scaling limits for equivariant Szego kernels

Fix a scheme $X$ over a field of characteristic zero that is equipped with an action of a reductive algebraic group $G$. We give necessary and sufficient conditions for a $G$-equivariant coherent sheaf on $X$ or a bounded-above complex of…

We consider the {\it concentration functions problem} for discrete quantum groups; we prove that if $\mathbb{G}$ is a discrete quantum group, and $\mu$ is an irreducible state in $l^1(\mathbb{G})$, then the convolution powers $\mu^n$,…

The rational Borel equivariant cohomology for actions of a compact connected Lie group is determined by restriction of the action to a maximal torus. We show that a similar reduction holds for any compact Lie group $G$ when there is a…

Let $G$ be a non-compact simple Lie group with Lie algebra $\mathfrak{g}$. Denote with $m(\mathfrak{g})$ the dimension of the smallest non-trivial $\mathfrak{g}$-module with an invariant non-degenerate symmetric bilinear form. For an…

Let $G$ a semisimple Lie group of non-compact type and let $\mathcal{X}_G$ be the Riemannian symmetric space associated to it. Suppose $\mathcal{X}_G$ has dimension $n$ and it has no factor isometric to either $\mathbb{H}^2$ or…

Let $X=U/K$ be a compact Hermitian symmetric space, and let $\sE$ be a $U$-homogeneous Hermitian vector bundle on $X$. In a previous paper, we showed that the space of nearly holomorphic sections is well-adapted for harmonic analysis in…

In this paper we search for conditions on a countably compact (pseudo-compact) topological semigroup under which: (i) each maximal subgroup $H(e)$ in $S$ is a (closed) topological subgroup in $S$; (ii) the Clifford part $H(S)$(i.e. the…

The space of unitary $C_{0}$-semigroups on separable infinite dimensional Hilbert space, when viewed under the topology of uniform weak convergence on compact subsets of $\mathbb{R}_{+}$, is known to admit various interesting residual…

We formulate a quantization commutes with reduction principle in the setting where the Lie group $G$, the symplectic manifold it acts on, and the orbit space of the action may all be noncompact. It is assumed that the action is proper, and…

We describe an extension at the level of the moduli space of stable spin curves of genus g of the map associating to an ineffective spin structure its Scorza curve (equivalently, the vanishing locus of its Szeg\H{o} kernel). We compute the…

For a proper action by a locally compact group $G$ on a manifold $M$ with a $G$-equivariant Spin-structure, we obtain obstructions to the existence of complete $G$-invariant Riemannian metrics with uniformly positive scalar curvature. We…

We study positive kernels on $X\times X$, where $X$ is a set equipped with an action of a group, and taking values in the set of $\mathcal A$-sesquilinear forms on a (not necessarily Hilbert) module over a $C^*$-algebra $\mathcal A$. These…

We consider actions of real Lie subgroups G of complex reductive Lie groups on Kaehlerian spaces. Our main result is the openness of the set of semistable points with respect to a momentum map and the action of G.

Let X be a hermitian manifold and let L^k be a high power of a hermitian line bundle over X. Local versions of Demailly's holomorphic Morse inequalities are presented - after integration they yield the usual inequalities. The local weak…

We present a general homotopical analysis of structured diagram spaces and discuss the relation to symmetric spectra. The main motivating examples are the I-spaces, which are diagrams indexed by finite sets and injections, and J-spaces,…

Given a connected semisimple Lie group $G$, Monod has recently proved that the measurable cohomology of the $G$-action $H^*_m(G \curvearrowright G/P)$ on the Furstenberg boundary $G/P$, where $P$ is a minimal parabolic subgroup, maps…

For a $\Gamma$--equivariant holomorphic Lie algebroid $(V,\, \phi)$, on a compact Riemann surface $X$ equipped with an action of a finite group $\Gamma$, we investigate the equivariant holomorphic Lie algebroid connections on holomorphic…

Let $\Gamma$ be a finite group acting on a Lie group $G$. We consider a class of group extensions $1 \to G \to \hat{G} \to \Gamma \to 1$ defined by this action and a $2$-cocycle of $\Gamma$ with values in the centre of $G$. We establish and…

We presented a Hilbert-Mumford criterion for polystablility associated with an action of a real reductive Lie group $G$ on a real submanifold $X$ of a Kahler manifold $Z$. Suppose the action of a compact Lie group with Lie algebra…

We get asymptotics for the volume of large balls in an arbitrary locally compact group G with polynomial growth. This is done via a study of the geometry of G and a generalization of P. Pansu's thesis. In particular, we show that any such G…