The metaplectic Shalika model and symmetric square L-function

One of the tools frequently used in the study of group representations and L-functions is called a model. Roughly speaking, a model is a unique realization of a representation in a convenient space of functions on the group. We will discuss examples of models on linear and covering groups. We will present a novel model: the metaplectic Shalika model. This is the analog of the Shalika model of GL(2n) of Jacquet and Shalika. One interesting representation having this model is the so-called exceptional representation of Kazhdan and Patterson, which is the analog for linear groups of the Weil representation. This representation is truly exceptional.  We will describe it and its role in the study of the symmetric square L-function, and related problems.