Hardening solutions are used with impression made of:
Agar impression material contains borax, which is a known retarder for setting of gypsum products. The gelation process of alginate impressions produces not only insoluble calcium alginate but also sodium sulfate, which is a gypsum-setting accelerator at low concentration, but becomes a retarder at a higher concentration. In addition, polysaccharide also inhibits the setting of gypsum. Because of retardation, the surfaces of the gypsum models prepared from hydrocolloid may be too soft for use as dies or casts.
The deficiency of gypsum setting can be overcome in two ways: 

By immersing the agar impression in a solution containing a gypsum accelerator, such as 2% potassium sulfate solution, prior to pouring the impression with the gypsum-forming product or
By incorporating a gypsum surface hardener in the material, such as the sulfate used in the formulation for agar hydrocolloid and the potassium titanium fluoride used in alginate.

Reference: PHILLIPS’ SCIENCE OF DENTAL MATERIALS, 12th ed page no 175
Hydrocolloid
Impression compound
Elastomer
Zinc oxide eugenol