Schur polynomials at roots of unity

Terry Gannon

York University

Abstract: My talk will be about certain finite sets of complex numbers which are remarkable for two reasons:

(i) There is a long list of diverse contexts in which they arise, such as elements of finite order in Lie groups, quantum groups at roots of 1, moduli spaces of semistable bundles over Riemann surfaces, Chevalley groups for Z/pZ, representation theory of Kac-Moody algebras,... (ii) They inherit from these algebraic contexts many symmetries and properties which makes the theorems and the proofs very pretty. The theory exploring these sets is still poorly developed, and there are many easy-to-understand open problems. I will develop at least one of these contexts, describe some of the known results, and state some of the open problems.