Antiorbital Complexes

Abstract

Let E be a finite dimensional vector space over an algebraic closure of a finite field with a given linear action of a connected linear algebraic group K and let E’ be the dual space. A complex of l-adic sheaves on E is said to be orbital if it is a simple perverse sheaf whose support is a single K-orbit. A complex of l-adic sheaves on E is said to be biorbital if it is orbital and if its Deligne Fourier transform is orbital on E’. In this talk we study examples of biorbital complexes arising in the case where E is an eigenspace of a semisimple automorphism of a reductive Lie algebra.

About the Speaker

Prof. George Lusztig is the Abdun-Nur Professor of Mathematics at Massachusetts Institute of Technology. He is a Fellow of the Royal Society of London, a Fellow of the American Academy of Arts and Sciences, and a Member of the US National Academy of Sciences. He was awarded the Berwick Prize (London Mathematical Society, 1977), the Cole Prize in Algebra (American Mathematical Society, 1985), and the Brouwer Medal (Dutch Mathematical Society, 1999) and the Leroy P. Steele Prize for Lifetime Achievement (American Mathematical Society, 2008).