کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4599834 | 1336825 | 2013 | 14 صفحه PDF | دانلود رایگان |
Let B be an n×nn×n nilpotent matrix with entries in an infinite field kk. The nilpotent commutator NBNB of B is known to be an irreducible algebraic variety. Assume that B is in Jordan canonical form with the associated Jordan block partition P and let Q(P)Q(P) be the Jordan partition of a generic element of NBNB. P. Oblak associated to a given partition P another partition resulting from a recursive process. She conjectured that this partition is the same as Q(P)Q(P). R. Basili, A. Iarrobino and the author later generalized the process introduced by Oblak. The main result of this paper states that all such processes give rise to the same partition – a partition that is defined in terms of the lengths of unions of special symmetric chains in a poset associated to NBNB. This poset was defined by P. Oblak as the digraph determined by the non-zero entries of a generic matrix in a maximal nilpotent subalgebra of NBNB.
Journal: Linear Algebra and its Applications - Volume 439, Issue 12, 15 December 2013, Pages 3763–3776