While Yukon is a territory constitutionally, our preference is to refer to simply “Yukon” rather than “the Yukon territory.” This reflects the devolution process that took place in 2003 when the Government of Yukon gained direct control over a much wider variety of provincial-type programs, responsibilities and powers.
Not: Yukon Territory, the Territory, Y.T.
But: Yukon, the territory
"YT" is the accepted abbreviation for "Yukon" but do not use it in communications materials. In fact, we encourage you to use "Yukon" all materials, including mailing addresses, as it's clearer and easier to read than "YT".
While many of us say “the Yukon” in conversation and in informal correspondence, when writing for publication use only “Yukon.”
Not: the Yukon
Not: Northwest Territories, N.W.T., NWT
But: the Northwest Territories, the NWT
Not: Any sort of abbreviation as there's no abbreviation for Nunavut.