Aspa o 1 is the key allergen associated with an allergy to asparagus, it is a lipid transfer protein (LTP). If you have an allergy to this protein you will still suffer symptoms on ingestion of the cooked vegetable.
There is some evidence that asparagus can cause contact dermatitis rashes – this is due to a plant growth inhibitor called 1,2,3-Trithiane-5-carboxylic acid, which is present in young shoots. If sensitised to this you will still be able to eat the cooked food.
I have put together some more comprehensive resources at http://www.allergyresources.co.uk/Asparagus.php
The allergy resources page for asparagus covers the key allergens, which allergic syndromes are linked to this allergy and other foods which are commonly cross reactive with asparagus.
There is also regularly updated links to useful websites specifically for asparagus allergies and the latest research papers on the topic.
If you have multiple allergies and are interested in how they are linked or want to find out more about food allergies outside the usual top 14 then you can follow me on Facebook or Twitter, where I share a food allergy card every day of the week.