Spin_c quantization and the K-multiplicities of the discrete series

Singular Reduction and Quantization

Consider a compact prequantizable symplectic manifold M on which a compact Lie group G acts in a Hamiltonian fashion. The ``quantization commutes with reduction'' theorem asserts that the G-invariant part of the equivariant index of M is equal to the Riemann-Roch number of the symplectic quotient of M, provided the quotient is nonsingular. We extend this result to singular symplectic quotients, using partial desingularizations of the symplectic quotient to define its Riemann-Roch number. By similar methods we also compute multiplicities for the equivariant index of the dual of a prequantum bun…

离散混合量子化

Discrete Mixed Quantization

本文为图向量丛开发了一种混合量子化技术，并将其应用于多个渐近谱问题，包括Alon-Boppana界、Kesten-McKay律、渐近行列式、量子遍历性、零因子收敛和Ramanujan向量丛。

Optimal Riemannian quantization with an application to air traffic analysis

The goal of optimal quantization is to find the best approximation of a probability distribution by a discrete measure with finite support. When dealing with empirical distributions, this boils down to finding the best summary of the data by a smaller number of points, and automatically yields a K-means-type clustering. In this paper, we introduce Competitive Learning Riemannian Quantization (CLRQ), an online algorithm that computes the optimal summary when the data does not belong to a vector space, but rather a Riemannian manifold. We prove its convergence and show simulated examples on the …