You probably need to check the guidelines for what is considered compensation. I believe, however, that the pension is a benefit you are receiving for previous work, and the qualifying indicators for UC are concerned with any earnings you worked for during the benefit week(s), regardless of when you will receive the income. Vacation pay and holiday pay may affect your UC benefit, but even that is discretionary.
Many states treat pensions differently. But, in general, if you qualify for benefits, and are ready, willing and able to work, you can collect. Some states make no differentiation at all. Others partially offset benefits by some formula tied to your pension. In some states it makes a difference who is paying the pension. If it was your most recent employer, there's a special formula for benefit reduction. Best thing to do is to type (Your State) Unemployment Compensation into your search engine, locate your state's site and check out the FAQ's. You'll most likely find the answer there.
Other option on Monday -- call your local unemployment compensation office for the information on how your state handles pensions.
