Dear Dan,
I am not so familiar with the Iwahori and Matsumoto set-up, but
I assume, as Nicolas mentioned before, this is equivalent to the
extended affine Weyl group, see for example Section 2.4 in
http://front.math.ucdavis.edu/0605.5451
By [Kac, Proposition 6.5] the affine Weyl group is a semid
There is an enlargement of the affine Hecke algebra,
due to Iwahori and Matsumoto, which I don't know how
to implement in Sage. This is an issue for type A,
related to the difference between GL_n and SL_n.
Let us consider the case of ['A',2,1]. If p is a
prime element in a nonarchimedean local fie
