On Riemann-Roch Formulas for Multiplicities

DOI10.1090/S0894-0347-96-00197-XzbMath0851.53020arXivalg-geom/9405014OpenAlexW1517189148MaRDI QIDQ4874241

Eckhard Meinrenken

Publication date: 10 November 1996

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/alg-geom/9405014

zbMATH Keywords

quantizationsymplectic reductionmultiplicities of representationsRiemann-Roch formulas

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Relations of PDEs on manifolds with hyperfunctions (58J15)

Related Items (33)

Spinc-quantization and the K-multiplicities of the discrete series ⋮ A vector partition function for the multiplicities of \(\mathfrak{sl}_k\mathbb C\) ⋮ \([Q,R=0\) and Kostant partition functions] ⋮ On geometric quantization of \(b\)-symplectic manifolds ⋮ Quantization commutes with reduction, a survey ⋮ Multiplicities formula for geometric quantization. I ⋮ Multiplicities formula for geometric quantization. II ⋮ Geometric quantization on CR manifolds ⋮ RR-BS correspondence—a localization phenomenon of the index in geometric quantization ⋮ On the geometric quantization of contact manifolds ⋮ Eigenvalue distributions of reduced density matrices ⋮ Torus fibrations and localization of index. III: Equivariant version and its applications ⋮ Symplectic reduction and Riemann-Roch formulas for multiplicities ⋮ Spectral asymptotics via the semiclassical Birkhoff normal form ⋮ A \(K\)-homological approach to the quantization commutes with reduction problem ⋮ Plethysm and lattice point counting ⋮ Moment maps and equivariant volumes ⋮ \(K\)-theory and the quantization commutes with reduction problem ⋮ 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 ⋮ Geometric quantization and families of inner products ⋮ Quantization of presymplectic manifolds and circle actions ⋮ Formal geometric quantization ⋮ Symplectic surgery and the Spin\(^c\)-Dirac operator ⋮ Relative Ding stability and an obstruction to the existence of Mabuchi solitons ⋮ Witten Non Abelian Localization for Equivariant K-Theory, and the [𝑄,𝑅=0 Theorem] ⋮ Advances in quantization: quantum tensors, explicit star-products, and restriction to irreducible leaves ⋮ Momentum maps and reduction in algebraic geometry ⋮ Quantization of polysymplectic manifolds ⋮ Convex polytopes and quantization of symplectic manifolds ⋮ The moduli space of Fano manifolds with Kähler-Ricci solitons

Cites Work

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• On the Kostant multiplicity formula
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• Two dimensional gauge theories revisited
• Elliptic operators and compact groups
• Polynômes arithmétiques et méthode des polyedres en combinatoire
• The Riemann-Roch theorem for complex V-manifolds
• Localization for nonabelian group actions
• Holomorphic slices, symplectic reduction and multiplicities of representations
• The index of elliptic operators. II
• The index of elliptic operators. III
• Heckman, Kostant, and Steinberg formulas for symplectic manifolds
• The Equivariant Index and Kirillov's Character Formula
• K-THEORETICAL INDEX THEOREMS FOR ORBIFOLDS

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