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

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

We classify all non-collapsing Curtis–Tits and Phan amalgams with 3- spherical diagram over all fields...

Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | THEOREM | KAC-MOODY GROUPS | Fields, Algebraic | Mathematical research | Finite groups | Models | Research | Amalgams | Graphic methods

Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | THEOREM | KAC-MOODY GROUPS | Fields, Algebraic | Mathematical research | Finite groups | Models | Research | Amalgams | Graphic methods

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

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

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

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

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

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

Non-equilibrium molecular dynamics simulations are employed in order to access the detailed atomic behavior of fluids moving in nanochannels and to quantify...

Biomedical Engineering | Engineering | Shear viscosity | Wall wettability | Analytical Chemistry | Moody’s diagram | Nanochannel flows | Nanotechnology and Microengineering | Engineering Fluid Dynamics | Friction factor | Wall roughness | MOLECULAR-DYNAMICS | TRANSPORT-PROPERTIES | PHYSICS, FLUIDS & PLASMAS | BEHAVIOR | SLIP | LIQUID | NANOSCIENCE & NANOTECHNOLOGY | Moody's diagram | ARGON | INSTRUMENTS & INSTRUMENTATION | KRYPTON

Biomedical Engineering | Engineering | Shear viscosity | Wall wettability | Analytical Chemistry | Moody’s diagram | Nanochannel flows | Nanotechnology and Microengineering | Engineering Fluid Dynamics | Friction factor | Wall roughness | MOLECULAR-DYNAMICS | TRANSPORT-PROPERTIES | PHYSICS, FLUIDS & PLASMAS | BEHAVIOR | SLIP | LIQUID | NANOSCIENCE & NANOTECHNOLOGY | Moody's diagram | ARGON | INSTRUMENTS & INSTRUMENTATION | KRYPTON

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

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

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

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

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

.... Similar to the Moody diagram for flow in pipes, a diagram for flow in a single rough fracture has been generated to relate the friction coefficient with Re and the roughness...

experimental study | variable rough‐walled fractures | groundwater flow | non‐Darcian flow | Moody diagram | Non-Darcian flow | Variable rough-walled fractures | Experimental study | Groundwater flow | PERMEABILITY | variable rough-walled fractures | WATER RESOURCES | MODEL | JOINTS | non-Darcian flow | TRANSPORT | HYDRAULIC CONDUCTIVITY | GROUNDWATER-FLOW | ROCK FRACTURES | NAVIER-STOKES | EQUATION | VALIDITY | Fracture mechanics | Law | Friction | Fluid dynamics | Reynolds number | Roughness | Fluid flow | Flux

experimental study | variable rough‐walled fractures | groundwater flow | non‐Darcian flow | Moody diagram | Non-Darcian flow | Variable rough-walled fractures | Experimental study | Groundwater flow | PERMEABILITY | variable rough-walled fractures | WATER RESOURCES | MODEL | JOINTS | non-Darcian flow | TRANSPORT | HYDRAULIC CONDUCTIVITY | GROUNDWATER-FLOW | ROCK FRACTURES | NAVIER-STOKES | EQUATION | VALIDITY | Fracture mechanics | Law | Friction | Fluid dynamics | Reynolds number | Roughness | Fluid flow | Flux

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

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

MATHEMATICS | PATHS | CRYSTAL BASES | KAC-MOODY ALGEBRAS | CHARACTER FORMULA

Journal Article

16.
Full Text
A geometric realization of spin representations and Young diagrams from quiver varieties

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

Young diagram | Clifford algebra | Geometrization | Quiver | Spin representation | MATHEMATICS | spin representation | KAC-MOODY ALGEBRAS | quiver | geometrization | INVARIANT-THEORY | ROOT SYSTEMS

Journal Article

Indian Journal of Science and Technology, ISSN 0974-6846, 2016, Volume 9, Issue 21

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

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

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

Indian Journal of Science and Technology, ISSN 0974-6846, 2016, Volume 9, Issue 25

Journal Article

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