The invariant measure with respect to the infinite-dimensional Cartan group and representations of the parabolic current group
Anatoly Vershik
Abstract
There is a unique up to scalar infinite-dimensional Lebesgue measure in the space of Schwartz distributions which is invariant under the infinite-dimensional Cartan group (see arXiv:0806.2215). That measure allows to define the representation of the current group of the maximal parabolic subgroups of the semisimple groups of rank 1 (arXiv:0809.1387). The model of the representation is completely different from the well-known model of Fock space.