14 citations · 70 across the 24 of their papers we have counts for
25 papers
Delocalized eta invariants of the signature operator on G-proper manifolds
Paolo Piazza, Hessel Posthuma, Yanli Song +1
Let be a connected, linear real reductive group and let be a cocompact -proper manifold without boundary. We define delocalized eta invariants associated to a -inve…
Symplectic reduction and a Darboux-Moser-Weinstein theorem for Lie algebroids
Yi Lin, Yiannis Loizides, Reyer Sjamaar +1
We extend the Marsden-Weinstein reduction theorem and the Darboux-Moser-Weinstein theorem to symplectic Lie algebroids. We also obtain a coisotropic embedding theorem for symplecti…
Riemannian foliations and geometric quantization
Yi Lin, Yiannis Loizides, Reyer Sjamaar +1
We introduce geometric quantization for constant rank presymplectic structures with Riemannian null foliation and compact leaf closure space. We prove a quantization-commutes-with-…
Cartan Motion Group and Orbital Integrals
Yanli Song, Xiang Tang
In this short note, we study the variation of orbital integrals, as traces on the group algebra , under the deformation groupoid. We show that orbital integrals are continuous u…
On the Connes-Kasparov isomorphism, I: The reduced C*-algebra of a real reductive group and the K-theory of the tempered dual
Pierre Clare, Nigel Higson, Yanli Song +1
This is the first of two papers dedicated to the computation of the reduced C*-algebra of a connected, linear, real reductive group up to Morita equivalence, and the verification o…
Higher orbital integrals, rho numbers and index theory
Paolo Piazza, Hessel Posthuma, Yanli Song +1
Let be a connected, linear real reductive group. We give sufficient conditions ensuring the well-definedness of the delocalized eta invariant associated to a Dirac…
Log symplectic manifolds and
Yi Lin, Yiannis Loizides, Reyer Sjamaar +1
We show, under an orientation hypothesis, that a log symplectic manifold with simple normal crossing singularities has a stable almost complex structure, and hence is Spin. In…
An index theorem for higher orbital integrals
Peter Hochs, Yanli Song, Xiang Tang
Recently, two of the authors of this paper constructed cyclic cocycles on Harish-Chandra's Schwartz algebra of linear reductive Lie groups that detect all information in the -th…
Higher Orbit Integrals, Cyclic Cocyles, and K-theory of Reduced Group C*-algebra
Yanli Song, Xiang Tang
Let G be a connected real reductive group. Orbit integrals define traces on the group algebra of G. We introduce a construction of higher orbit integrals in the direction of higher…
Geometric quantization of b-symplectic manifolds
Maxim Braverman, Yiannis Loizides, Yanli Song
We introduce a method of geometric quantization for compact -symplectic manifolds in terms of the index of an Atiyah-Patodi-Singer (APS) boundary value problem. We show further…
A KK-theoretic perspective on deformed Dirac operators
Yiannis Loizides, Rudy Rodsphon, Yanli Song
We study the index theory of a class of perturbed Dirac operators on non-compact manifolds of the form , where is a Clifford mul…
Norm-square localization and the quantization of Hamiltonian loop group spaces
Yiannis Loizides, Yanli Song
In an earlier article we introduced a new definition for the `quantization' of a Hamiltonian loop group space , involving the equivariant -index of a Dirac-type o…
A geometric formula for multiplicities of -types of tempered representations
Peter Hochs, Yanli Song, Shilin Yu
Let be a connected, linear, real reductive Lie group with compact centre. Let be compact. Under a condition on , which holds in particular if is maximal compact, w…
Quantization of Hamiltonian loop group spaces
Yiannis Loizides, Yanli Song
We prove a Fredholm property for spin-c Dirac operators on non-compact manifolds satisfying a certain condition with respect to the action of a semi-direct product gro…
Spinor modules for Hamiltonian loop group spaces
Yiannis Loizides, Eckhard Meinrenken, Yanli Song
Let be the loop group of a compact, connected Lie group . We show that the tangent bundle of any proper Hamiltonian -space has a natural completion $\over…
A geometric realisation of tempered representations restricted to maximal compact subgroups
Peter Hochs, Yanli Song, Shilin Yu
Let be a connected, linear, real reductive Lie group with compact centre. Let be maximal compact. For a tempered representation of , we realise the restriction $π|…
An equivariant index for proper actions II: properties and applications
Peter Hochs, Yanli Song
In the first part of this series, we defined an equivariant index without assuming the group acting or the orbit space of the action to be compact. This allowed us to generalise an…
An equivariant index for proper actions I
Peter Hochs, Yanli Song
Equivariant indices have previously been defined in cases where either the group or the orbit space in question is compact. In this paper, we develop an equivariant index without a…
On the Vergne conjecture
Peter Hochs, Yanli Song
Consider a Hamiltonian action by a compact Lie group on a possibly noncompact symplectic manifold. We give a short proof of a geometric formula for decomposition into irreducible r…
Dirac operators on quasi-Hamiltonian G-spaces
Yanli Song
We develop notions of twisted spinor bundle and twisted pre-quantum bundle on quasi-Hamiltonian G-spaces. The main result of this paper is that we construct a Dirac operator with i…
Equivariant indices of Spin-Dirac operators for proper moment maps
Peter Hochs, Yanli Song
We define an equivariant index of Spin-Dirac operators on possibly noncompact manifolds, acted on by compact, connected Lie groups. The main result in this paper is that the in…
An equivariant index for proper actions III: the invariant and discrete series indices
Peter Hochs, Yanli Song
We study two special cases of the equivariant index defined in part I of this series. We apply this index to deformations of Spin-Dirac operators, invariant under actions by po…
Formal Verlinde Module
Yanli Song
Let G be a compact, simple and simply connected Lie group and $\A$ be an equivariant Dixmier-Douady bundle over G. For any fixed level k, we can define a G-C*-algebra $C_{\A^{k+h}}…
A K-homological approach to the quantization commutes with reduction problem
Yanli Song
Kasparov defined a distinguished K-homology fundamental class, so called the Dirac element. We prove a localization formula for the Dirac element in K-homology of crossed product o…