On Thu, Dec 10, 2009 at 02:22:25PM -0800, Daniel Bump wrote: > I am doing some calculations in Iwahori Hecke algebras. > By this I mean the deformation of the group algebra of > a Weyl group in which the generators corresponding to > the simple reflections satisfy t_alpha^2=(q-1)*t_alpha+q, > where q is a deformation parameter. > > For type A a version is implemented in Sage as > HeckeAlgebraSymmetricGroupT. > > Does there exist a SAGE implementation for other Weyl groups?
As strange as this may sound, not yet! I guess we did too much 0-Hecke *monoids* with Florent and Anne lately :-) That being said, the Hecke algebra of the symmetric group badly needs a serious refactoring to use the category code. The design is pretty clear: http://wiki.sagemath.org/HeckeAlgebras; it's time to get started on this topic! I think rewriting from scratch an implementation of the generic Hecke algebra in the T_w basis, with two parameters q1 and q2 would be a good starting point. With the current category and root system stuff, it should be about 20 lines of code. Starting with the example in AlgebrasWithBasis, I would add the following functions: def mult_basis_by_generator(w, i) # Multiplication of T_w by T_i def mult_by_generator(x, i): # Multiplication of x in the Hecke algebra by T_i (done by # applying the previous by linearity def mult_on_basis(u, v): # Multiplication of T_u by T_v, recursively along a reduced word for v Let me know if you need help! Cheers, Nicolas -- Nicolas M. Thiéry "Isil" <nthi...@users.sf.net> http://Nicolas.Thiery.name/ -- 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.
