The relation between polymer models at zero temperature and characters of the general linear group GLn(R) has been known since the ﬁrst breakthroughs in the ﬁeld around the KPZ universality through the works of Johansson, Baik, Rains, Okounkov and others. Later on, geometric liftings of the GLn(R) characters ap-peared in the study of positive temperature polymer models in the form of GLn(R)-Whittaker functions. In this talk I will describe joint works with E. Bisi where we have established that Whittaker functions associated to the orthogonal group SO2n+1(R) can be used to describe laws of positive temperature polymers when their end point is free to lie on a line. Going back to zero temperature, we will also see that characters of other classical groups such as SO2n+1(R),Sp2n(R),SO2n(R) do play a role in describing laws of polymers in various geometries. This occurence might be surprising given the length of time these models have been studied.