Orbit closures in the enhanced nilpotent cone
Orbit closures in the enhanced nilpotent cone
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DOI：
10.1016/j.aim.2008.04.008
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发表时间：
2007-12
影响因子：
1.7
通讯作者：
Pramod N. Achar;A. Henderson
中科院分区：
文献类型：
--
作者：
Pramod N. Achar;A. Henderson
本文研究了G=GL（V）在增强幂零锥V×N中的轨道，其中N是V的幂零自同态簇，这些轨道由n=dimV的双分拆参数化，并证明了闭包序对应于双分拆上的自然偏序.此外，我们证明了局部相交上同调的轨道闭包是由某些bipartition类似的Kostka多项式，定义的Shoji。最后，我们将C型Kato奇异幂零锥与C型Kato奇异幂零锥联系起来，证明了C型Kato奇异幂零锥的闭包序是相同的，并证明了C型Kato奇异幂零锥的交上同调是相同的，但度是加倍的。
We study the orbits of G=GL(V) in the enhanced nilpotent cone V×N, where N is the variety of nilpotent endomorphisms of V. These orbits are parametrized by bipartitions of n=dimV, and we prove that the closure ordering corresponds to a natural partial order on bipartitions. Moreover, we prove that the local intersection cohomology of the orbit closures is given by certain bipartition analogues of Kostka polynomials, defined by Shoji. Finally, we make a connection with Kato's exotic nilpotent cone in type C, proving that the closure ordering is the same, and conjecturing that the intersection cohomology is the same but with degrees doubled.