Actually I am an undergraduate student, but I want to study Heisenberg groups over arbitrary field. 

Firstly, why is this group important? I know that the Heisenberg group is important in the field of quantum physics, but in mathematics how is it? And secondly I want to know the current studies of the classifications of the irreducible representations of Heisenberg groups over an arbitrary field(like over $\mathbb{Q}_p,\mathbb{R}, \mathbb{C}$ or finite field). Would you recommend any references in this area? (e.g. survey papers or influential papers)

Thanks.