The metaplectic Shalika model and symmetric square L-function

One of the pillars of the Langlands program is L-functions. We will recall Artin‘s L-functions, then briefly describe the modern automorphic point of view. 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 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 of a cover of GL(n), which is the analog 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.