A hereditary theorem for rigid and pseudorigid components of Lusztig's nilpotent varieties in type $A$

Erez Lapid; Mark Shusterman

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arXiv · 2609.06601

A hereditary theorem for rigid and pseudorigid components of Lusztig's nilpotent varieties in type $A$

Erez Lapid·Mark Shusterman

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Abstract

For irreducible components $C_σ$ of Lusztig's nilpotent varieties of type $A$ with graded dimension $(1,2,\dots,n,n-1,\dots,1)$ arising from permutations $σ\in S_n$, we characterize the property that $C_σ\oplus C_σ$ is an irreducible component combinatorially in terms of $σ$. The permutations that occur, which we call \emph{pseudosmooth}, are described by a recursion on direct sums and deleting suitable corners, whose terminal cases are the permutations obtained from \[ 3412,\quad 4231,\quad 35142,\quad 42513,\quad 45312,\quad 426153,\quad 463152,\quad 526413 \] by inflating the entries into consecutive decreasing blocks. The main new input is a hereditary property valid for decompositions of multisegments with disjoint extreme points.

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Erez Lapid, Mark Shusterman. 2026-09-06. A hereditary theorem for rigid and pseudorigid components of Lusztig's nilpotent varieties in type $A$. https://arxiv.org/abs/2609.06601

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