Hi Nicolas, Travis has already answered Q1. I was going to say Yes because; if it holds in one basis then it holds in all bases (which I suspect you had in mind when you formulated the question); then it holds in the canonical basis in the strong sense that applying a lowering operator gives 0 or another basis element.
If I understand you correctly, you are studying the coordinate ring on n x r matrices. If so, then you may want to use the basis of bideterminants. Invariant theory, Young bitableaux and combinatorics Advances in Math. (27) 1978 Best, Bruce -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/d/optout.
