Some results on genuine representations of double cover of GL(2) - part I

We begin by quick recollection of the representation theory of GL(2) over a p-adic field, then introduce the double cover of GL(2) and provide both general results concerning the representations of this group and discuss principal series representation and the Weil representation, which yields in particular
a cuspidal representation under some conditions. We will mainly follow the following texts: (1) Gelbart: Weils representation and the spectrum of the metaplectic group, LNM 530 (2) Gelbart and Piatetski-Shapiro: Distinguished Representations and Modular forms of half-integral weight, Invent. Math, 59, 1990, 145-188.