scholarly journals Nilpotent orbit Coulomb branches of types AD

2019 ◽  
Vol 2019 (2) ◽  
Author(s):  
Amihay Hanany ◽  
Dominik Miketa
Keyword(s):  
Nilpotent Orbit

scholarly journals W algebras, cosets and VOAs for 4d $$ \mathcal{N} $$ = 2 SCFTs from M5 branes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Dan Xie ◽  
Wenbin Yan
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Nilpotent Orbit ◽  
Vertex Operator Algebras ◽  
Flavor Symmetries ◽  
Conformal Embedding

Abstract We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the W algebras defined using nilpotent orbit with partition [qm, 1s]. Gauging above AD matters, we can find VOAs for more general $$ \mathcal{N} $$ N = 2 SCFTs engineered from 6d (2, 0) theories. For example, the VOA for general (AN − 1, Ak − 1) theory is found as the coset of a collection of above W algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory.

On the Maximal Primitive Ideal Corresponding to the Model Nilpotent Orbit

2012 ◽  
Vol 2012 (24) ◽  
pp. 5731-5743 ◽  
Author(s):  
Hung Yean Loke ◽  
Gordan Savin
Keyword(s):  
Nilpotent Orbit ◽  
Primitive Ideal

scholarly journals WREATH PRODUCTS, NILPOTENT ORBITS AND SYMPLECTIC DEFORMATIONS

2007 ◽  
Vol 18 (05) ◽  
pp. 473-481
Author(s):  
BAOHUA FU
Keyword(s):  
Wreath Product ◽  
Wreath Products ◽  
Nilpotent Orbit ◽  
Nilpotent Orbits ◽  
Symplectic Resolutions

We recover the wreath product X ≔ Sym 2(ℂ2/± 1) as a transversal slice to a nilpotent orbit in 𝔰𝔭6. By using deformations of Springer resolutions, we construct a symplectic deformation of symplectic resolutions of X.

scholarly journals Tangent loci and certain linear sections of adjoint varieties

2000 ◽  
Vol 158 ◽  
pp. 63-72
Author(s):  
Hajime Kaji ◽  
Osami Yasukura
Keyword(s):  
Lie Algebra ◽  
Projective Variety ◽  
Linear Subspace ◽  
Nilpotent Orbit ◽  
Contact Type ◽  
Simple Lie Algebra ◽  
Veronese Variety ◽  
Linear Sections

AbstractAn adjoint variety X(g)associated to a complex simple Lie algebra is by definition a projective variety in ℙ*(g) obtained as the projectivization of the (unique) non-zero, minimal nilpotent orbit in g. We first describe the tangent loci of X(g) in terms of triples. Secondly for a graded decomposition of contact type we show that the intersection of X(g) and the linear subspace ℙ*(g1) in ℙ*(g) coincides with the cubic Veronese variety associated to g.

scholarly journals On the minimal modules for exceptional Lie algebras: Jordan blocks and stabilizers

2016 ◽  
Vol 19 (1) ◽  
pp. 235-258 ◽  
Author(s):  
David I. Stewart
Keyword(s):  
Algebraic Group ◽  
Lie Algebras ◽  
Nilpotent Orbit ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Exceptional Lie Algebras ◽  
Induced Module ◽  
Simply Connected

Let $G$ be a simple simply connected exceptional algebraic group of type $G_{2}$, $F_{4}$, $E_{6}$ or $E_{7}$ over an algebraically closed field $k$ of characteristic $p>0$ with $\mathfrak{g}=\text{Lie}(G)$. For each nilpotent orbit $G\cdot e$ of $\mathfrak{g}$, we list the Jordan blocks of the action of $e$ on the minimal induced module $V_{\text{min}}$ of $\mathfrak{g}$. We also establish when the centralizers $G_{v}$ of vectors $v\in V_{\text{min}}$ and stabilizers $\text{Stab}_{G}\langle v\rangle$ of $1$-spaces $\langle v\rangle \subset V_{\text{min}}$ are smooth; that is, when $\dim G_{v}=\dim \mathfrak{g}_{v}$ or $\dim \text{Stab}_{G}\langle v\rangle =\dim \text{Stab}_{\mathfrak{g}}\langle v\rangle$.

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 Cohomology of the Minimal Nilpotent Orbit

2008 ◽  
Vol 13 (2) ◽  
pp. 355-387 ◽  
Author(s):  
Daniel Juteau
Keyword(s):  
Nilpotent Orbit

Support varieties of baby Verma modules

2018 ◽  
Vol 17 (11) ◽  
pp. 1850211
Author(s):  
Yiyang Li ◽  
Bin Shu ◽  
Yufeng Yao
Keyword(s):  
Verma Module ◽  
Nilpotent Orbit ◽  
Closed Field ◽  
Verma Modules ◽  
Prime Characteristic ◽  
Reductive Algebraic Group ◽  
Type Formula ◽  
Coxeter Number ◽  
Support Variety ◽  
Support Varieties

Let [Formula: see text] be a connected reductive algebraic group over an algebraically closed field [Formula: see text] of prime characteristic [Formula: see text] and [Formula: see text]. For a given nilpotent [Formula: see text]-character [Formula: see text], let [Formula: see text] be a baby Verma module associated with a restricted weight [Formula: see text]. A conjecture describing the support variety of [Formula: see text] via that of its restricted counterpart is given: [Formula: see text]. Under the assumption of [Formula: see text](the Coxeter number) and [Formula: see text] [Formula: see text]-regular, this conjecture is proved when [Formula: see text] falls in the regular nilpotent orbit for any [Formula: see text] and the subregular nilpotent orbit for [Formula: see text] being of type [Formula: see text]. We also verify this conjecture whenever [Formula: see text] is of type [Formula: see text] and [Formula: see text] falls in the minimal nilpotent orbit.

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