I am working light duty while recovering from my work injury, and my employer is paying me $10.00 per hour instead of my regular $20.00 per hour. Can they do that?

Yes, they can, but you are owed temporary partial disability benefits, or TPD benefits.  TPD benefits are paid if the employee is able to perform some work during the rehabilitation period.  These benefits are typically paid if the employee is released to light duty while still receiving medical treatment, and the employer provides light duty work, but at a lower rate of pay. The worker can be paid benefits equal to 2/3 of the difference between the average earnings prior to the accident and the amount which the employee is able to earn during the disability. 

For instance, if the employee's pre-injury pay was $800 per week, but the employer is only paying the employee $400 per week while the employee does light duty work, the employer/work comp insurer owes the employee the following: $800 - $400 = $400 week difference.  2/3 of $400 = $266.67.  Therefore,  temporary partial disability benefits should be paid in the amount of $266.67.