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A hereditary theorem for rigid and pseudorigid components of Lusztig's nilpotent varieties in type A
Abstract
For irreducible components Cσ of Lusztig's nilpotent varieties of type A with graded dimension (1,2,…,n,n−1,…,1) arising from permutations σ∈ Sn, we characterize the property that Cσ⊕ Cσ 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, 4231, 35142, 42513, 45312, 426153, 463152, 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.
Related
- Socle formulas for rigid irreducible components of Lusztig's nilpotent varieties in type A
- Two-step nilpotent monodromy of local systems on special varieties
- Counting Irreducible Components of the Semistable Global Nilpotent Cone
- A Balian-Low theorem for nilpotent Lie groups
- Molnár's Theorem for split C*-by-nilpotent algebras
BibTeX
@misc{lapid2026hereditary,
title = {{A hereditary theorem for rigid and pseudorigid components of Lusztig's nilpotent varieties in type $A$}},
author = {Erez Lapid and Mark Shusterman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06601},
eprint = {2609.06601},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06601},
}
RIS
TY - UNPB
TI - A hereditary theorem for rigid and pseudorigid components of Lusztig's nilpotent varieties in type A
AU - Erez Lapid
AU - Mark Shusterman
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06601
UR - https://arxiv.org/abs/2609.06601
AB - For irreducible components C_σ of Lusztig's nilpotent varieties of type A with graded dimension (1,2,…,n,n−1,…,1) arising from permutations σ∈ S_n, we characterize the property that C_σ⊕ 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, 4231, 35142, 42513, 45312, 426153, 463152, 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.
ER -