Quantized Reduced Fusion Elements and Kostant’s Problem

Paper in proceeding, 2014

We find a partial solution to the problem of Kostant concerning description of the locally finite endomorphisms of highest weight irreducible modules. The solution is obtained by means of its reduction to an extension of the quantization problem. While the classical quantization problem consists in finding ⋆-product deformations of the commutative algebras of functions, we consider the q-case when the initial object is already a noncommutative algebra.