Abstract: It was shown by Karpenko that the upper bound <br>
for the canonical dimension of a linear algebraic groups <br>
is given by the degree of a certain unimodular cycle in <br>
the complete flag variety. We extend the concept of such <br>
unimodular degree to an arbitrary Kac-Moody flag. We <br>
discuss various combinatorial applications and computations<br>
of such invariant. <br>
This is a recent work in progress with Edward Richmond.