Can anyone explain what Iwahori order is? All I know is that it is mentioned [here](https://mathoverflow.net/questions/3483/intuitive-example-of-a-jacobson-radical/3490#3490).



Explanation and Definition of Iwahori order
To translate Rob's answer above, you take a ring $R$ and ideal $I$, and take the ring of consisting of matrices with coefficients in $R$ such that the image in $R/I$ is upper-triangular. This is a subring of all matrices. 


The name "Iwahori order" is borrowed from the name "Iwahori subgroup" which refers to the invertible elements in this ring (usually in the case where R is a valuation ring, and I the valuation ideal).


