scholarly journals Quiver theories and formulae for nilpotent orbits of Exceptional algebras

2017 ◽  
Vol 2017 (11) ◽  
Author(s):  
Amihay Hanany ◽  
Rudolph Kalveks
Keyword(s):  
Nilpotent Orbits ◽  
Exceptional Algebras

scholarly journals Folding orthosymplectic quivers

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Antoine Bourget ◽  
Julius F. Grimminger ◽  
Amihay Hanany ◽  
Rudolph Kalveks ◽  
Marcus Sperling ◽  
...  
Keyword(s):  
Phase Diagrams ◽  
Moduli Spaces ◽  
Nilpotent Orbits ◽  
Gauge Groups ◽  
Unitary Gauge ◽  
General Family ◽  
New Family ◽  
New Construction ◽  
Exceptional Algebras

Abstract Folding identical legs of a simply-laced quiver creates a quiver with a non-simply laced edge. So far, this has been explored for quivers containing unitary gauge groups. In this paper, orthosymplectic quivers are folded, giving rise to a new family of quivers. This is realised by intersecting orientifolds in the brane system. The monopole formula for these non-simply laced orthosymplectic quivers is introduced. Some of the folded quivers have Coulomb branches that are closures of minimal nilpotent orbits of exceptional algebras, thus providing a new construction of these fundamental moduli spaces. Moreover, a general family of folded orthosymplectic quivers is shown to be a new magnetic quiver realisation of Higgs branches of 4d $$ \mathcal{N} $$ N = 2 theories. The Hasse (phase) diagrams of certain families are derived via quiver subtraction as well as Kraft-Procesi transitions in the brane system.

Complexity and nilpotent orbits

1994 ◽  
Vol 83 (1) ◽  
pp. 223-237 ◽  
Author(s):  
Dmitrii I. Panyushev
Keyword(s):  
Nilpotent Orbits

Nilpotent Orbits in Simple Lie Algebras and their Transverse Poisson Structures

2008 ◽  
Author(s):  
P. A. Damianou ◽  
H. Sabourin ◽  
P. Vanhaecke ◽  
Rui Loja Fernandes ◽  
Roger Picken
Keyword(s):  
Lie Algebras ◽  
Poisson Structures ◽  
Nilpotent Orbits ◽  
Simple Lie Algebras

scholarly journals NILPOTENT ORBITS AND CODIMENSION-2 DEFECTS OF 6d${\mathcal N} = (2, 0)$ THEORIES

2013 ◽  
Vol 28 (03n04) ◽  
pp. 1340006 ◽  
Author(s):  
OSCAR CHACALTANA ◽  
JACQUES DISTLER ◽  
YUJI TACHIKAWA
Keyword(s):  
Lie Algebra ◽  
Young Diagram ◽  
Central Charge ◽  
Outer Automorphism ◽  
Natural Generalization ◽  
Nilpotent Orbits ◽  
Coulomb Branch ◽  
Local Properties

We study the local properties of a class of codimension-2 defects of the 6d [Formula: see text] theories of type J = A, D, E labeled by nilpotent orbits of a Lie algebra [Formula: see text], where [Formula: see text] is determined by J and the outer-automorphism twist around the defect. This class is a natural generalization of the defects of the six-dimensional (6d) theory of type SU (N) labeled by a Young diagram with N boxes. For any of these defects, we determine its contribution to the dimension of the Higgs branch, to the Coulomb branch operators and their scaling dimensions, to the four-dimensional (4d) central charges a and c and to the flavor central charge k.

Octonions and subalgebras of the exceptional algebras

1989 ◽  
Vol 30 (3) ◽  
pp. 585-593 ◽  
Author(s):  
F. Buccella ◽  
A. Della Selva ◽  
A. Sciarrino
Keyword(s):  
Exceptional Algebras

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.

SPECTRAL DECOMPOSITION OF R-MATRICES FOR EXCEPTIONAL LIE ALGEBRAS

1991 ◽  
Vol 06 (10) ◽  
pp. 923-927 ◽  
Author(s):  
S.M. SERGEEV
Keyword(s):  
Lie Algebras ◽  
Spectral Decomposition ◽  
Spectral Decompositions ◽  
Exceptional Lie Algebras ◽  
Exceptional Algebras ◽  
Vector Representations

In this paper spectral decompositions of R-matrices for vector representations of exceptional algebras are found.

scholarly journals Nilpotent orbits of exceptional Lie algebras over algebraically closed fields of bad characteristic

1985 ◽  
Vol 38 (3) ◽  
pp. 330-350 ◽  
Author(s):  
D. F. Holt ◽  
N. Spaltenstein
Keyword(s):  
Finite Field ◽  
Lie Algebras ◽  
Closed Field ◽  
Nilpotent Orbits ◽  
Reductive Algebraic Group ◽  
Exceptional Lie Algebras ◽  
Closed Fields ◽  
Characteristic 3 ◽  
Algebraically Closed Fields

AbstractThe classification of the nilpotent orbits in the Lie algebra of a reductive algebraic group (over an algebraically closed field) is given in all the cases where it was not previously known (E7 and E8 in bad characteristic, F4 in characteristic 3). The paper exploits the tight relation with the corresponding situation over a finite field. A computer is used to study this case for suitable choices of the finite field.

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