Kleinian Singularities: Some Geometry, Combinatorics and Representation Theory

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

We review the relationship between discrete groups of symmetries of Euclidean three-space, constructions in algebraic geometry around Kleinian singularities including versions of Hilbert and Quot schemes, and their relationship to finite-dimensional and affine Lie algebras via the McKay correspondence. We focus on combinatorial aspects, such as the enumeration of certain types of partition-like objects, reviewing in particular a recently developed root-of-unity-substitution calculus. While the most complete results are in type A, we also develop aspects of the theory in type D, and end with some questions about the exceptional type E cases.

OriginalspracheEnglisch
Seiten (von - bis)213-247
Seitenumfang35
FachzeitschriftJahresbericht der Deutschen Mathematiker-Vereinigung
Jahrgang126
Ausgabenummer4
DOIs
PublikationsstatusVeröffentlicht - Dez. 2024

ÖFOS 2012

  • 101001 Algebra
  • 101009 Geometrie

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