Level-rank duality via tensor categories
arXiv:1208.5131 · doi:10.1007/s00220-013-1869-9
Abstract
We give a new way to derive branching rules for the conformal embedding $$(\asl_n)_m\oplus(\asl_m)_n\subset(\asl_{nm})_1.$$ In addition, we show that the category $\Cc(\asl_n)_m^0$ of degree zero integrable highest weight $(\asl_n)_m$-representations is braided equivalent to $\Cc(\asl_m)_n^0$ with the reversed braiding.
16 pages, to appear in Communications in Mathematical Physics. Version 2 changes: Proof of main theorem made explicit, example 4.11 removed, references updated