Proving properties of metaplectic groups without using explicit cocycle I learned the metaplectic group from the book of Gelbart, Weil's representation and the spectrum of the metaplectic group. It seems to me that most of the properties of the metaplectic group are proved by using the explicit cocycle given in Section 2.1.
For example, the local metaplectic group (i.e. double cover of $SL(2)$) splits over the maximal compact subgroup, as long as the residual characteristic is greater than $2$; it does not split over the maximal torus; and the global metaplectic group splits over $SL(2,F)$; etc.
Is it always necessary to go back to the cocycle description to prove these properties?
 A: For covering groups of $SL(2)$ there are nice formulas for the cocyle, and it is helpful to use them. For other groups, especially outside of the symplectic group $Sp(2n)$, it is much more difficult to work with explicit cocycles. Nevertheless there is a rich theory of these groups. For example see Matsumoto's Sur les sous-groupes arithmétiques des groupes semi-simples déployés (Ann. Scient. Éc. Norm. Sup. 1969) or G. Prasad and Rapinchuk, Computation of the Metaplectic Kernel (IHES 1996).
A: A more recent treatment of covering groups is due to Brylinski-Deligne (Central Extensions of Reductive Groups by $K_2$, Publ. Math. Inst. Hautes Études Sci. No. 94 (2001)), where the data of the covering group is given in terms of linear algebra.  A nice introduction to these ideas is in an article of Gan-Gao (available here: http://www.math.nus.edu.sg/~matgwt/L-BD-(2016-July-final.pdf ).  In particular, one can prove various properties of metaplectic groups using data which is simpler to handle than the explicit cocycle (e.g. bilinear/quadratic forms).  
