Formal Geometric Quantization III, Functoriality in the spin-c setting

In this paper, we prove a functorial aspect of the formal geometric quantization procedure of non-compact spin-c manifolds

Quillen's relative Chern character is multiplicative

In the 80's, Quillen constructed a de Rham relative cohomology class associated to a smooth morphism between vector bundles, that we call the relative Quillen Chern character. In the first part of this paper we prove the multiplicativ property of the relative Quillen Chern character. Then we obtain a Riemann-Roch formula between the relative Chern character of the Bott morphism and the relative Thom form.Comment: 28 pages. This article will appear in the proceedings of the conference "Algebraic Analysis and Around" in honour of Professor Masaki Kashiwara's 60's birthda

Kirillov's orbit method: the case of discrete series representations

Let V be an Harish-Chandra discrete series representation of a real semi-simple Lie group G' and let G be a semi-simple subgroup of G'. In this paper, we give a geometric expression of the G-multiplicities in V when the representation V is supposed to be G-admissible

On the structure of K_G(T_G M)

In this expository paper, we revisit the results of Atiyah-Singer and de Concini-Procesi-Vergne concerning the structure of the K-theory groups K_G(T_G M)