We show that in ADE type the trace of Webster's categorification a tensor product irreducibles for quantum group is isomorphic to Weyl modules current algebra U˙(g[t]). This extends result Beliakova, Habiro, Lauda, and Webster who showed categorified U˙⁎(g) U˙(g[t]), cyclotomic quotient U˙⁎(g), which categorifies single irreducible group, module use deformation argument based on technique unfur...

Proposition 1. M is injective if and only if its singular value decomposition M = UDV H has a V that is square and invertible. In this case, MM is invertible and M = (MHM)−1MH . Proof. Let M be an r × c matrix. Suppose that M is injective, so that rank(M) = c because the kernal is zero. Then D is a c × c matrix and so V H is also c× c. V H must already be injective (lest M not be injective), an...