This is one of those cases where there are two hostas with the same name. One is registered and, therefore, the "official" version of H. 'Green Wedge' while the other is a non-registered plant and needs to be renamed to avoid further confusion.

"Plants in commerce under this name differ. Bob Solberg reports two different plants: one introduced by Roy Klehm; the other originated in Paul Aden's garden. The Aden cultivar was registered without description in 1976, and it was not until 1988 that an official description was published. This plant is a selected clone or an F1 selfed seedling of H. nigrescens 'Elatior'..."
 

This plant is an open-pollinated hybrid of H. nigrescens which was originally registered by Paul Aden of New York in 1978. In 2012, the registration was modified to show the originator as Florence Shaw of Massachusetts.

It forms a giant size plant about 27 inches high by 60 inches wide. The shiny, light green foliage is heart shaped at the base and lacks corrugation or waviness. Its petioles are deep purple-red in color. Light lavender flowers bloom from late July into August.

According to The Hostapedia by Mark Zilis (2009), "Like 'Green Sheen', 'Green Wedge' impresses observers for its large-size, shiny, bright green foliage...It has been a good source of seedlings and would be a great addition to any breeding program."

Hosta Helper will call this plant 'Green Wedge' (Shaw)
 

This non-registered cultivar was introduced by Klehm Nursery but was subsequently withdrawn for the market. However, Schmid (1991) says, "...there are many examples of this choice cultivar in gardens, which now should be renamed H. 'Green Wedge Klehm'."

This plant is a large size hosta about 22 inches high by 40 inches wide with very light green foliage. The cordate, flat leaves are pruinose above and whitish below. It bears white, bell-shaped flowers on 22 inch tall scapes in July followed by viable seeds.

Hosta Helper will call this plant 'Green Wedge' (Klehm)