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Advances in Mathematics, ISSN 0001-8708, 12/2014, Volume 267, pp. 225 - 276
We show that the fixed-point subvariety of a Nakajima quiver variety under a diagram automorphism is a disconnected union of quiver varieties... 
Springer resolution | Quiver varieties | Automorphisms | Slodowy slices | ALE SPACES | REPRESENTATIONS | KAC-MOODY ALGEBRAS | GRAPHS | MATHEMATICS | SPRINGER CORRESPONDENCE | CONSTRUCTION | SKEW GROUP-ALGEBRAS | GEOMETRY | Algebra | Mathematics - Representation Theory
Journal Article
Israel Journal of Mathematics, ISSN 0021-2172, 3/2019, Volume 230, Issue 1, pp. 97 - 140
Journal Article
Journal of Algebra, ISSN 0021-8693, 2006, Volume 301, Issue 1, pp. 112 - 147
An extended Vogan diagram is an extended Dynkin diagram with a diagram involution, such that the vertices fixed by the involution can be painted or unpainted... 
Almost compact real form | Kac–Moody Lie algebra | Extended Vogan diagram | Kac-Moody Lie algebra | MATHEMATICS | MOODY LIE-ALGEBRAS | extended Vogan diagram | REAL FORMS | almost compact real form
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 04/2010, Volume 362, Issue 4, pp. 1721 - 1750
A Vogan diagram is a set of involution and painting on a Dynkin diagram. It selects a real form, or equivalently an involution, from a complex simple Lie algebra... 
Algebra | Mathematical theorems | Diagrams | Subalgebras | Mathematical vectors | Automorphisms | Algebraic conjugates | Commuting | Vertices | simple Lie algebra | MATHEMATICS | REAL FORMS | Dynkin diagram | MOODY LIE-ALGEBRAS | locally symmetric pair | involution | Vogan diagram
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 04/2010, Volume 43, Issue 15, pp. 155209 - 155209
We give a criterion for a Dynkin diagram, equivalently a generalized Cartan matrix, to be symmetrizable... 
KAC-MOODY ALGEBRAS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | BILLIARDS | Equivalence | Mathematical analysis | Roots | Classification | Proving | Orbits | Criteria
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 01/2009, Volume 239, Issue 1, pp. 65 - 88
A Vogan diagram is a Dynkin diagram of a Kac-Moody Lie algebra of finite or affine type overlayed with additional structures... 
Vogan diagram | Twisted affine Kac-Moody algebra | Almost compact real forms | MATHEMATICS | CLASSIFICATION | twisted affine Kac-Moody algebra | almost compact real forms | REAL FORMS
Journal Article
Journal of Algebra, ISSN 0021-8693, 2004, Volume 279, Issue 1, pp. 22 - 37
A Vogan diagram is a Dynkin diagram with an involution, and the vertices fixed by the involution may be painted... 
Graph painting | Dynkin diagram | Simple Lie algebra | Vogan diagram | simple Lie algebra | MATHEMATICS | REAL FORMS | Dynkm diagram | MOODY LIE-ALGEBRAS | graph painting
Journal Article
Microfluidics and Nanofluidics, ISSN 1613-4982, 1/2016, Volume 20, Issue 1, pp. 1 - 7
Journal Article
Communications in Algebra, ISSN 0092-7872, 11/2006, Volume 34, Issue 11, pp. 3903 - 3933
We continue the study of stabilization phenomena for Dynkin diagram sequences initiated in the earlier work of Kleber and the present author... 
Tensor product multiplicity | Littelmann path model | Branching multiplicity | Partial order on dominant weights | MATHEMATICS | tensor product multiplicity | KAC-MOODY ALGEBRAS | branching multiplicity | partial order on dominant weights
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 07/2018, Volume 222, Issue 7, pp. 1606 - 1627
We introduce the affine Vogan diagrams of complex simple Lie algebras. These are generalizations of Vogan diagrams, and we study the involutions represented... 
MATHEMATICS | MATHEMATICS, APPLIED | MOODY LIE-ALGEBRAS | REAL FORMS | SPACES
Journal Article
Journal of Algebra, ISSN 0021-8693, 11/2001, Volume 245, Issue 1, pp. 395 - 412
We prove that the Lakshmibai–Seshadri paths fixed by a diagram automorphism ω of a Kac–Moody algebra can be identified with the Lakshmibai... 
MATHEMATICS | KAC-MOODY ALGEBRAS | DEMAZURE CHARACTER FORMULA
Journal Article
Mathematics (Basel), ISSN 2227-7390, 03/2019, Volume 7, Issue 3, p. 253
The Colebrook-White equation is often used for calculation of the friction factor in turbulent regimes; it has succeeded in attracting a great deal of... 
turbulent flow | friction factor | explicit solutions | moody diagram | maximum deviation
Journal Article
Hydrological Processes, ISSN 0885-6087, 02/2011, Volume 25, Issue 4, pp. 614 - 622
Journal Article
Journal of Algebra, ISSN 0021-8693, 2002, Volume 251, Issue 1, pp. 461 - 474
We show that the standard paths and the standard monomials fixed by a diagram automorphism for a Kac... 
MATHEMATICS | KAC-MOODY ALGEBRAS
Journal Article
Journal of Algebra, ISSN 0021-8693, 2003, Volume 268, Issue 1, pp. 343 - 365
We define actions of a diagram automorphism on certain crystals, and then study three kinds of “extremal... 
MATHEMATICS | PATHS | CRYSTAL BASES | KAC-MOODY ALGEBRAS | CHARACTER FORMULA
Journal Article
Journal of Algebra, ISSN 0021-8693, 2006, Volume 297, Issue 1, pp. 186 - 207
.... In doing so, we give an explicit parametrization of the irreducible components of Nakajima varieties of type D in terms of Young diagrams... 
Young diagram | Clifford algebra | Geometrization | Quiver | Spin representation | MATHEMATICS | spin representation | KAC-MOODY ALGEBRAS | quiver | geometrization | INVARIANT-THEORY | ROOT SYSTEMS
Journal Article
Journal of Algebra, ISSN 0021-8693, 01/2017, Volume 469, pp. 390 - 401
... if it is Hermitian. We use the Vogan diagrams to classify the Hermitian real forms, and show that their symmetric spaces carry complex structures... 
Affine Kac–Moody Lie algebras | Admissible positive systems | Hermitian real forms | VOGAN DIAGRAMS | MATHEMATICS | Affine Kac-Moody Lie algebras | REAL FORMS | AUTOMORPHISMS | Algebra
Journal Article
Forum Mathematicum, ISSN 0933-7741, 11/2017, Volume 29, Issue 6, pp. 1413 - 1427
We prove that the periodic quantum Toda lattice corresponding to any extended Dynkin diagram is completely integrable... 
37N20 | 17B35 | Periodic quantum Toda lattice | Kac–Moody Lie algebras | foldings of Dynkin diagrams | 37K10 | complete integrability | Kac-Moody Lie algebras | MATHEMATICS | MATHEMATICS, APPLIED | MECHANICAL SYSTEMS | Homology
Journal Article
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