标题： 奇异的斯帕伦斯坦流形 显示英文标题

标题： Exotic Spaltenstein varieties

摘要： 我们定义了一类新的代数簇，称为奇异Spaltenstein簇。 这些簇推广了Spaltenstein簇的概念（这些是经典Springer纤维的partial flag类比）到奇异Springer纤维的情况。 我们证明了，对于二阶自伴幂零自同态，最高维的不可约分支通过构造一个显式映射与半标准Young双表一一对应。 此外，我们能够给出这个最高维的组合公式。 我们猜想，这种不可约分支的描述对任意阶的幂零自同态都成立。 最后，我们提到一些与Robinson-Schensted-Knuth对应的关系。 显示英文摘要

摘要： We define a new family of algebraic varieties, called exotic Spaltenstein varieties. These generalise the notion of Spaltenstein varieties (which are the partial flag analogues to classical Springer fibres) to the case of exotic Springer fibres. We show that, for self-adjoint nilpotent endomorphisms of order two, the top-dimensional irreducible components are in bijection with semi-standard Young bitableaux, via constructing an explicit map. Moreover, we are able to give a combinatorial formula for this top dimension. We conjecture that this description of the irreducible components holds for nilpotent endomorphisms of arbitrary order. Finally, we mention some connections to the Robinson-Schensted-Knuth correspondence.