Singular reduction and quantization
From MaRDI portal
Publication:1292709
DOI10.1016/S0040-9383(98)00012-3zbMath0928.37013arXivdg-ga/9707023OpenAlexW2054842419MaRDI QIDQ1292709
Reyer Sjamaar, Eckhard Meinrenken
Publication date: 13 December 1999
Published in: Topology (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/dg-ga/9707023
Lie groupHamiltonian dynamicsequivariant indexsymplectic quotientHamiltonian manifoldsRiemann-Roch numberprequantum line bundleprequantizable symplectic manifold
Related Items
Spinc-quantization and the K-multiplicities of the discrete series ⋮ \([Q,R=0\) and Kostant partition functions] ⋮ Symplectic reduction along a submanifold ⋮ The equivariant Riemann-Roch theorem and the graded Todd class ⋮ Singular equivariant asymptotics and Weyl's law. On the distribution of eigenvalues of an invariant elliptic operator ⋮ Quantisation commutes with reduction at discrete series representations of semisimple groups ⋮ Symplectic implosion and nonreductive quotients ⋮ Formal geometric quantisation for proper actions ⋮ Quantization commutes with reduction, a survey ⋮ Computation of dilated Kronecker coefficients ⋮ Singular cotangent bundle reduction and polar actions ⋮ Reductions for branching coefficients ⋮ The index of leafwise \(G\)-transversally elliptic operators on foliations ⋮ Some conditions for descent of line bundles to GIT quotients \((G/B\times G/B\times G/B)//G\) ⋮ GEOMETRIC QUANTIZATION OF HAMILTONIAN ACTIONS OF LIE ALGEBROIDS AND LIE GROUPOIDS ⋮ Residue formulae for vector partitions and Euler-Maclaurin sums. ⋮ RR-BS correspondence—a localization phenomenon of the index in geometric quantization ⋮ Riemannian foliations and geometric quantization ⋮ Multiplicity formulas for fundamental strings of representations of classical Lie algebras ⋮ On the asymptotics of Kronecker coefficients. ⋮ A geometric realisation of tempered representations restricted to maximal compact subgroups ⋮ Eigenvalue distributions of reduced density matrices ⋮ Generalized Littlewood-Richardson coefficients for branching rules of \(\mathrm{GL}(n)\) and extremal weight crystals ⋮ The multiplicities of the equivariant index of twisted Dirac operators ⋮ Kirillov's formula and Guillemin-Sternberg conjecture ⋮ Intersection cohomology of quotients of nonsingular varieties ⋮ INTERSECTION THEORY ON SYMPLECTIC QUOTIENTS OF PRODUCTS OF SPHERES ⋮ Polarized orbifolds associated to quantized Hamiltonian torus actions ⋮ On the Vergne conjecture ⋮ Plethysm and lattice point counting ⋮ Pre-quantization of the moduli space of flat \(G\)-bundles over a surface ⋮ Obstructions to combinatorial formulas for plethysm ⋮ Centered complexity one Hamiltonian torus actions ⋮ Dimension of zero weight space: an algebro-geometric approach ⋮ Moment maps and equivariant volumes ⋮ On the cohomology of a polarization which contains the generators of a free torus action. ⋮ Geometric quantization for proper moment maps: the Vergne conjecture ⋮ Quasi-polynomials and the singular \([Q,R=0\) theorem] ⋮ Localization of the Riemann-Roch character ⋮ On geometric quantization of \(b^m\)-symplectic manifolds ⋮ Formal geometric quantization. III: Functoriality in the \(\mathrm{spin}^c\) setting ⋮ Kirillov's orbit method: the case of discrete series representations ⋮ Proof of Stembridge's conjecture on stability of Kronecker coefficients ⋮ Box splines, tensor product multiplicities and the volume function ⋮ Quantization commutes with singular reduction: Cotangent bundles of compact Lie groups ⋮ Geometric quantization and families of inner products ⋮ Quantization of presymplectic manifolds and circle actions ⋮ Norm-square localization and the quantization of Hamiltonian loop group spaces ⋮ Formal geometric quantization ⋮ INTERSECTION COHOMOLOGY OF REPRESENTATION SPACES OF SURFACE GROUPS ⋮ Geometric quantization for proper moment maps ⋮ QUANTIZATION OF SINGULAR REDUCTION ⋮ Witten Non Abelian Localization for Equivariant K-Theory, and the [𝑄,𝑅=0 Theorem] ⋮ A geometric formula for multiplicities of 𝐾-types of tempered representations ⋮ Momentum maps and reduction in algebraic geometry ⋮ Quantisation of presymplectic manifolds, $K$-theory and group representations ⋮ Quantization of polysymplectic manifolds ⋮ Coarse geometry and Callias quantisation ⋮ Lie groupoids and Lie algebroids in physics and noncommutative geometry ⋮ Quantization commutes with reduction in the non-compact setting: the case of holomorphic discrete series ⋮ Vector partition functions and Kronecker coefficients