In my textbook I have this list of irregular verbs:

 Infinitive  Present Simple  Past Simple    Past Participle
     go          go             went            gone
     do          do             did             done
     be          is             was             been
     be          am             was             been
     be          are            were            been
     have        have           had             had
     will        will           would           would

As can be seen from the table, the present-simple forms of verbs coincide with their infinitives, except in case with the verb "be".

Thus, the infinitive of the present-simple "do" is also "do", and the infinitive of the present-simple "will" is also "will".

I wonder what form of "will" exactly we are dealing with in the following sentence:

These days they will not allow us to walk into that room.

Why? (Please, explain the logic in your answer)