I have a simplicity 7119 hydrostatic mower with a 48" mower deck. What is the correct belt length to get?

Drive belt broken or slipped of pulleys, hydrostatic drive filter(s) plugged. Should be one or those, Roger. Follow the drivebelt with your hand (disconnect battery to be safe) and see if it hasn't slipped off the engine drive pulley, idler pulleys, or axle pulley. If you tractor is hydrostat, may be time to replace filter.

Since you mentioned "48-inch riding mower" let's assume your question is about the mower deck and not the overall mower or its main drive belt (if manual shift-on-the-fly model). If the belt burns that means it is running but slipping against something; or that the drive sheave us turning against an impeded belt. In the first case the belt will be burned along its length; in the second the burning will be occuring in one location(s) along the belt. In any case of belt slippage, check first that all tensioners (springs) are properly in place and not broken or fatigued and in need of replacement. The only other thing would be resistance to belt running, such as:
blade blockage; blade rotor resistance from lack of grease or ruined bearing in need of replacment; grass clogging on deck underside or under blade drive pulley on deck top side; a pully sheave out of round; an obstacle between belt and sheave that is preventing free turn of sheave and belt run; misrouted belt; an overstretched belt that cannot be sufficiently tensioned. Inspect and correct or replace as needed.

Looks like 5/8 x 90"

HI,

The simplicity has a a two point mounting system for the deck. It attaches to the front axle which has two runners that go to the front axle's rear support bracket.

Closely check the runners near where the pins that hold the mower deck. They are known for cracking and breakage. Secondly, closely check the decks metal center support bracket, it bolts to the center of the deck and supports the idler pulleys as well as the deck alignment and mounting. Those, too, are known to crack near the front just behind the front pulley.

Just in case anyone else comes across this in searching for a Main Drive Belt or a Deck Belt :-

Marksman Industrial Ltd
Main Drive Belt 1134.9013-01 (see also 9585-0057-00)
External length 888 mm
"STIGA 1134-9013-01 Equivalent Belt" Kevlar reinforced

Deck Belt 1134.9032-01 (see also 9585-0075-00)
External Length 1219 mm, Pitch Length 1206 mm
4L480K - 1/2" x 48" Kevlar reinforced

Note:
Stiga Garden Combi is pretty much an identical mower

Hope this helps someone.

most wear parts numbers are on the bottom side of the hood.

Looking at the IPL(exploded parts list) will give you a good look at the route of the belt. Here is a link to use and find your model
http://www.husqvarna.com/us/support/download-manuals/?query=yth2348&types=I&brands=

Go to john deer dealer they should be able to print u of that diagram for you.

Try pulling back on the left foot pedal. This manually adjusts the drive belt tension and is a sign that the engine pulley has worn to the point the belt looses traction. A local repairman told me this last week and mine works fine now although in the very near future I'll need to replace the pully. Good luck