(1) Comments on "Quantum generalization of the Horn
conjecture", vol 21, number 2, JAMS 2008

The definition of dim \mathcal{I} in (2.2) page 372: This is meant to be the expected dimension of the intersection (2.1), therefore in the formula (2.2),

dim Gr(d,r,Z_{D,n}) is meant to be the expected dimension \chi (d,r,D-d,n-r) (which is the dimension if Gr(d,r,Z_{D,n}) is non-empty by Prop 2.2).

To avoid any confusion, please replace dim Gr(d,r,Z_{D,n}) in equations (2.2) and (2.3) by \chi(d,r,D-d,n-r) =r(n-r) + d(n-r) - (D-d)r.

(2) Unitarity of the KZ/Hitchin connection on conformal blocks in genus 0 for arbitrary Lie algebras.

The following correction should be made to the paragraph following Definition 3.1: add the hypothesis that the tensor product of \lambda_i

has a non-zero invariant. And remove the parenthetical comment of
evaluating on H_{\alpha_p}. The definition of dim \mathcal{I} in (2.2) page 372: This is meant to be the expected dimension of the intersection (2.1), therefore in the formula (2.2),

dim Gr(d,r,Z_{D,n}) is meant to be the expected dimension \chi (d,r,D-d,n-r) (which is the dimension if Gr(d,r,Z_{D,n}) is non-empty by Prop 2.2).

To avoid any confusion, please replace dim Gr(d,r,Z_{D,n}) in equations (2.2) and (2.3) by \chi(d,r,D-d,n-r) =r(n-r) + d(n-r) - (D-d)r.

(2) Unitarity of the KZ/Hitchin connection on conformal blocks in genus 0 for arbitrary Lie algebras.

The following correction should be made to the paragraph following Definition 3.1: add the hypothesis that the tensor product of \lambda_i