This name is a synonym of Luzula multiflora subsp. frigida (Buchenau) V.I.Krecz..
The record derives from IOPI
(data supplied on 2012-03-23)
which reports it as a synonym (record 453915) with original publication details: Fl. Aleutian Isl. 125 1937.
This name record (from IOPI) was not included in version 1 of The Plant List. It is possible the same name was included from a different data source, to check this you can search for Luzula multiflora in version 1 of The Plant List.