Title : A REMARK ON THE VARIETIES OF SUBSPACES STABLE UNDER A NILPOTENT TRANSFORMATION Authors : Maeda, Takashi Authors alternative : 前田, 髙士前田, 高士 Issue Date : 30-Dec-2007 Abstract : For a nilpotent linear transformation $f:V\to V$ of type $\lambda$ let $S(V,T)$ be the set of $f$-stable subspaces $W$ associated to an LR (Littlewood-Richardson)-tableau $T$, i.e. $W$'s such that dim $f^{r-1}V\cap f^{t-1}W/\langle f^rV\cap f^{t-1}W,f^{r-1}\cap f^tW\rangle$ is equal to the number of cells (squares) of $T$ filled with the letter $t$ in the $r$th row for all $t$ and $r$. Let $G(\lambda)$ be the subgroup of GL($V$) consisting of elements commuting with $f$. It is given an example of $S(V,T)$ that does not have a dense $G(\lambda)$-orbit. Type Local : 紀要論文 ISSN : 1344-008X Publisher : Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus URI : http://hdl.handle.net/20.500.12000/5027 Citation : Ryukyu mathematical journal Vol.20 p.1 -8 Appears in Collections : Vol.20 (2007)