  We develop the theory of colored bosonic models (initiated by Borodin and
Wheeler). We will show how a family of such models can be used to represent the
values of Iwahori vectors in the "spherical model" of representations of
$GL_r(F)$, where $F$ is a nonarchimedean local field. Among our results are a
monochrome factorization, which is the realization of the Boltzmann weights by
fusion of simpler weights, a local lifting property relating the colored models
with uncolored models, and an action of the affine Hecke algebra on the
partition functions of a particular family of models by Demazure-Lusztig
operators. As an application of the local lifting property we reprove a theorem
of Korff evaluating the partition functions of the uncolored models in terms of
Hall-Littlewood plynomials. Our results are very closely parallel to the theory
of fermionic models representing Iwahori Whittaker functions developed by
Brubaker, Buciumas, Bump and Gustafsson, with many striking relationships
between the two theories, confirming the philosophy that the spherical and
Whittaker models of principal series representations are dual.
