Canonical Bases in Certain Tensor Products

Abstract

24.1.1. Let M,M ∈ C be such that either ^ωM ∈ C^hi or M ∈ C^hi (see 3.4.7). We regard M ⊗ M naturally as a U ⊗ U-module and we define a linear map $\Theta$ : M ⊗ M →M ⊗ M by $\Theta$

(m ⊗ m ) = ∑ _ν $\Theta$

_ν (m ⊗ m ) (notation of 4.1.2.) This is well-defined since only finitely many terms of the sum are non-zero.