Lecture notes on the K-theory of the flag variety and the Fomin-Kirillov quadratic algebra

10. Lecture notes on the K-theory of the flag variety and the Fomin-Kirillov quadratic algebra (with C. Lenart), 2004. We construct a commutative subalgebra of the Fomin-Kirillov quadratic algebra and explain the (conjectural) connection to the K-theory ring of the flag variety and the associated Schubert structure constants. Update (Feb 12, 2006): 1. My coauthor C. Lenart has reported on our work in his paper "K-theory of the flag variety and the Fomin-Kirillov quadratic algebra" (published in the Journal of Algebra). 2. Conjecture 3.5 of our text above (as also reported in Lenart's paper) has been proved by A.N. Kirillov and T. Maeno (published in IMRN).