Hello, I'm looking at what I would like to do in Cernay, and I found new things about groups and group actions... but perhaps some of the stuff is implemented somewhere. I will complete the wiki on that topic just before the begining of the week. If you have any comment, please do.
1) The sage.groups.class_function.ClassFunction wraps the corresponding GAP's object. The class is nice because we are in particular able to decompose any class function as a sum of characters! But a bad point is that the class function is not an element of an algebra. In particular we can neither multiply a class function by a scalar nor add two class functions! * In Sage, should we consider the class functions with coefficients in R as the "dual" of the center of R[G] ? * Somebody knows how does the relation between group algebra and characters work in GAP ? 2) If G is a finite group and O x G -> G a finite G-action, then there is a natural permutation character associated to it (pi(g) = # nb of fixed point of g). The functions is quite generic and may be put very high in the hierarchy. Where ? Which name is the best adapted ? O.character() ? 3) The SymmetricGroup is currently implemented as a right action. But it appears that I need the natural diagonal action of G x G on (G / H) x (H \ G) (first factor acts on left and second factor on the right). Is there a way to handle that or is still in the todo list ? Cheers, Vincent -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.
