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...

The injective tensor product of normal representable bimodules over von Neumann algebras is shown to be normal. The usual Banach module projective tensor product of central representable bimodules over an Abelian C∗-algebra is shown to be representable. A normal version of the projective tensor product is introduced for central normal bimodules.