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Socle formulas for rigid irreducible components of Lusztig's nilpotent varieties in type $A$

Lapid, Erez et al.
arXiv (All) · Papers
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algebraic-geometryrepresentation-theory
Let $F$ be a non-archimedean local field. For any irreducible component $C$ of a nilpotent variety of type $A$ let $π(C)$ be the irreducible representation of a general linear group over $F$ attached to it. We show that if the multisegment of $C$ is multiplicity free, $C$ is rigid if and only if $π(
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