Subregular representations of $\sl_n$ and simple singularities of type $A

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60760Alexander Premet has stated the following problem: what is a relation between subregular nilpotent representations of a classical semisimple restricted Lie algebra and non-commutative deformations of the corresponding singularities? We solve this problem for type $A$. Using the McKay correspondence, we relate the solution to bases in equivariant $K$-theory introduced by Lusztig.34 pagesRepresentation TheoryAlgebraic GeometryQuantum AlgebraRings and Algebras17B50, 14J17, 16S32, 18F30Subregular representations of $\sl_n$ and simple singularities of type $A_{n-1}$text