G. Williamson - Character formulas in the modular representation theory of algebraic groups
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2018-06-25

I will review present two formulas for the characters of representations of reductive algebraic groups in positive characteristic p. Both formulas involve certain polynomials ("p-Kazhdan-Lusztig polynomials") which measure the failure of the decomposition theorem for resolutions of affine Schubert varieties, when the sheaf coefficients are of characteristic p. These formulas are proven under mild bounds on p (e.g. p ≥ 2 × Coxeter number) and are expected to hold uniformly. (This is joint work with S. Riche, with parts also joint with P. Achar and S. Makisumi.)