scholarly journals Generic singularities of nilpotent orbit closures

2017 ◽  
Vol 305 ◽  
pp. 1-77 ◽  
Author(s):  
Baohua Fu ◽  
Daniel Juteau ◽  
Paul Levy ◽  
Eric Sommers
Keyword(s):  
Nilpotent Orbit ◽  
Orbit Closures ◽  
Generic Singularities

scholarly journals JOSEPH IDEALS AND LISSE MINIMAL -ALGEBRAS

2016 ◽  
Vol 17 (2) ◽  
pp. 397-417 ◽  
Author(s):  
Tomoyuki Arakawa ◽  
Anne Moreau
Keyword(s):  
Nilpotent Orbit ◽  
Vertex Algebras ◽  
Orbit Closure ◽  
New Family ◽  
Orbit Closures

We consider a lifting of Joseph ideals for the minimal nilpotent orbit closure to the setting of affine Kac–Moody algebras and find new examples of affine vertex algebras whose associated varieties are minimal nilpotent orbit closures. As an application we obtain a new family of lisse ($C_{2}$-cofinite)$W$-algebras that are not coming from admissible representations of affine Kac–Moody algebras.

Nilpotent Orbit Varieties and the Atomic Decomposition of the Q-Kostka Polynomials

1998 ◽  
Vol 50 (3) ◽  
pp. 525-537 ◽  
Author(s):  
William Brockman ◽  
Mark Haiman
Keyword(s):  
Atomic Decomposition ◽  
Jordan Block ◽  
Geometric Interpretation ◽  
Nilpotent Orbit ◽  
Cohomology Rings ◽  
Direct Sum ◽  
Kostka Polynomials ◽  
Orbit Closures ◽  
Direct Sum Decomposition ◽  
Coordinate Rings

AbstractWe study the coordinate rings of scheme-theoretic intersections of nilpotent orbit closures with the diagonal matrices. Here μ′ gives the Jordan block structure of the nilpotent matrix. de Concini and Procesi [5] proved a conjecture of Kraft [12] that these rings are isomorphic to the cohomology rings of the varieties constructed by Springer [22, 23]. The famous q-Kostka polynomial is the Hilbert series for the multiplicity of the irreducible symmetric group representation indexed by λ in the ring . Lascoux and Schützenberger [15, 13] gave combinatorially a decomposition of as a sum of “atomic” polynomials with non-negative integer coefficients, and Lascoux proposed a corresponding decomposition in the cohomology model.Our work provides a geometric interpretation of the atomic decomposition. The Frobenius-splitting results of Mehta and van der Kallen [19] imply a direct-sum decomposition of the ideals of nilpotent orbit closures, arising from the inclusions of the corresponding sets. We carry out the restriction to the diagonal using a recent theorem of Broer [3]. This gives a direct-sum decomposition of the ideals yielding the , and a new proof of the atomic decomposition of the q-Kostka polynomials.

scholarly journals Normality of orbit closures in the enhanced nilpotent cone

2011 ◽  
Vol 203 ◽  
pp. 1-45 ◽  
Author(s):  
Pramod N. Achar ◽  
Anthony Henderson ◽  
Benjamin F. Jones
Keyword(s):  
Nilpotent Orbit ◽  
Complete Intersections ◽  
Quiver Variety ◽  
Quiver Varieties ◽  
Nilpotent Cone ◽  
Orbit Closures ◽  
Special Cases

AbstractWe continue the study of the closures of GL(V)-orbits in the enhanced nilpotent cone V × N begun by the first two authors. We prove that each closure is an invariant-theoretic quotient of a suitably defined enhanced quiver variety. We conjecture, and prove in special cases, that these enhanced quiver varieties are normal complete intersections, implying that the enhanced nilpotent orbit closures are also normal.

scholarly journals Normality of orbit closures in the enhanced nilpotent cone

2011 ◽  
Vol 203 ◽  
pp. 1-45 ◽  
Author(s):  
Pramod N. Achar ◽  
Anthony Henderson ◽  
Benjamin F. Jones
Keyword(s):  
Nilpotent Orbit ◽  
Complete Intersections ◽  
Quiver Variety ◽  
Quiver Varieties ◽  
Nilpotent Cone ◽  
Orbit Closures ◽  
Special Cases

AbstractWe continue the study of the closures of GL(V)-orbits in the enhanced nilpotent coneV × Nbegun by the first two authors. We prove that each closure is an invariant-theoretic quotient of a suitably defined enhanced quiver variety. We conjecture, and prove in special cases, that these enhanced quiver varieties are normal complete intersections, implying that the enhanced nilpotent orbit closures are also normal.

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