Journées SL2R à Reims 2018

Asymptotics of characters and associated cycles of Harish-Chandra modules

19 oct. 2018, 11:30

50m

Amphi 2 (UFR Sciences)

Exposé

Orateur

Salah Mehdi (Université de Lorraine (Metz))

Description

Abstract: We describe a translation principle for the Dirac index of virtual $(\mathfrak{g},K)$-modules. To each coherent family of such modules we attach a polynomial, on the dual of the compact Cartan subalgebra, which expresses the dependence of the leading term in the Taylor expansion of the character of the modules. Finally we will explain how this polynomial is related to the multiplicities of the associated cycle of certain Harish-Chandra modules. These results are joint with P. Pandžić, D. Vogan and R. Zierau.