Brendan Pawlowski 

Title: Maximal products of symmetric double cosets in a compact Lie group

Abstract: Consider the following problem: characterize pairs x,y in a compact Lie group G such that KxK*KyK = G, where K is the fixed-point subgroup of an involutive automorphism of G. I'll explain how to derive a necessary condition on x,y from combinatorial properties of the root system of (G,K) and its affine Weyl group. In the cases where G = SU(n) and K is the orthogonal group O(n), the compact symplectic group Sp(n/2), or the block-diagonal group S(U(n/2) x U(n/2)), this necessary condition turns out to be sufficient, and I'll explain why quantum Schubert calculus comes into the proof of this statement. I'll also give some motivation from quantum computing for considering this problem. No background on Lie group theory or quantum computing or will be assumed.