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 field, consider the group generated by
s1: [0 1 0] [1 0 0] [0 0 1] s2: [1 0 0] [0 0 1] [0 1 0] s0: [ 0 0 1/p] [ 0 1 0] [ p 0 0] This group is isomorphic to what you get with WeylGroup(['A',2,1]). Now Iwahori and Matsumoto enlarge this group with another element t: [0 1 0] [0 0 1] [p 0 0] For this they introduce a "generalized Tits system" with a Weyl group having nonidenty elements of length 0. For example t has length 0. Conjugating s0, s1, s2 by this permutes them cyclically. This is a fairly important type of Weyl group. It is not a Coxeter group. My question: what is the best approach to constructing such a group using Sage? Dan -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To post to this group, send email to sage-combinat-de...@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.
