Parabolic Induction and Geometry of Orbital Varieties for GL(n)

Abstract

Ariki and Ginzburg, after the previous work of Zelevinsky on orbital varieties, proved that multiplicities in a total parabolically induced representations are given by the value at q=1 of Kazhdan-Lusztig Polynomials associated to the symmetric groups. In my thesis I explore the geometry of orbital varieties and I essentially obtain two important results: - first I prove a conjecture of Zelevinksy on a property of independence of total parabolically induced representations. - More crucially I give a strategy to compute multiplicities in general parabolically induced representations using the product of perverse sheaves introduced by Lusztig.