Description of B-orbit closures of order 2 in upper-triangularmatrices

摘要: Let ${\mathfrak n}_n({\mathbb C})$ be the algebra of strictly upper-triangular $n\times n$ matrices and let ${\mathcal X}_2=\{u\in {\mathfrak C})\mid u^{2}=0\}$ subset nilpotent order 2. ${\bf B}_n({\mathbb group invertible acting on n}_n$ by conjugation. B}_u$ orbit $u\in{\mathcal X}_2$ with respect to this action. S}_n^2$ involutions in symmetric S}_n.$ We define a new partial which gives combinatorial description closure B}_u.$ also construct an ideal I}({\mathcal B}_u)\subset S({\mathfrak n}^*)$ whose variety V}({\mathcal B}_u))$ equals $\overline{\mathcal apply these results orbital varieties 2 s}{\mathfrak l}_n({\mathbb give complete such terms Young tableaux. definition up taking radical.