  In this work we discuss some appearances of semi-infinite combinatorics in
representation theory. We propose a semi-infinite moment graph theory and we
motivate it by considering the (not yet rigorously defined) geometric side of
the story. We show that it is possible to compute stalks of the local
intersection cohomology of the semi-infinite flag variety, and hence of spaces
of quasi maps, by performing an algorithm due to Braden and MacPherson.
