Search results for "Representation theory"

showing 10 items of 197 documents

On the irreducibility of Hurwitz spaces of coverings with an arbitrary number of special points

2013

In this paper we study Hurwitz spaces of coverings of Y with an arbitrary number of special points and with monodromy group a Weyl group of type D_d, where Y is a smooth, complex projective curve. We give conditions for which these spaces are irreducible.

Hurwitz spaces Weyl groups special points monodromy braid movesProjective curvePure mathematicsWeyl groupHurwitz quaternionGeneral MathematicsType (model theory)Algebrasymbols.namesakeMonodromyHurwitz's automorphisms theoremsymbolsIrreducibilitySettore MAT/03 - GeometriaMathematics::Representation TheoryMathematicsFilomat
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"Figure 8b" of "Production of (anti-)$^3$He and (anti-)$^3$H in p-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV"

2020

Coalescence parameter $B_3$ calculated using the average of $\mathrm{INEL}>0$ $^3\mathrm{H}$ and $^3\overline{\mathrm{H}}$ yields

InclusiveP PB --> ANTITRIT XRapidity Dependence5020Coalescence parameterMathematics::Representation TheoryTransverse Momentum DependenceP PB --> TRIT XB3
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"Figure 8a" of "Production of (anti-)$^3$He and (anti-)$^3$H in p-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV"

2020

Coalescence parameter $B_3$ calculated using the average of $\mathrm{INEL}>0$ $^3\mathrm{He}$ and $^3\overline{\mathrm{He}}$ yields

InclusiveRapidity DependenceP PB --> ANTIHE3 X5020Coalescence parameterMathematics::Representation TheoryP PB --> HE3 XTransverse Momentum DependenceB3
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Variations on Weyl's theorem

2006

AbstractIn this note we study the property (w), a variant of Weyl's theorem introduced by Rakočević, by means of the localized single-valued extension property (SVEP). We establish for a bounded linear operator defined on a Banach space several sufficient and necessary conditions for which property (w) holds. We also relate this property with Weyl's theorem and with another variant of it, a-Weyl's theorem. We show that Weyl's theorem, a-Weyl's theorem and property (w) for T (respectively T*) coincide whenever T* (respectively T) satisfies SVEP. As a consequence of these results, we obtain that several classes of commonly considered operators have property (w).

Intersection theoremDiscrete mathematicsWeyl's theoremsPure mathematicsPicard–Lindelöf theoremProperty (w)Applied MathematicsLeast-upper-bound propertyBanach spaceLocalized SVEPBounded operatorDanskin's theoremBrowder's theoremsMathematics::Representation TheoryBrouwer fixed-point theoremBounded inverse theoremAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Explainable Reinforcement Learning with the Tsetlin Machine

2021

The Tsetlin Machine is a recent supervised machine learning algorithm that has obtained competitive results in several benchmarks, both in terms of accuracy and resource usage. It has been used for convolution, classification, and regression, producing interpretable rules. In this paper, we introduce the first framework for reinforcement learning based on the Tsetlin Machine. We combined the value iteration algorithm with the regression Tsetlin Machine, as the value function approximator, to investigate the feasibility of training the Tsetlin Machine through bootstrapping. Moreover, we document robustness and accuracy of learning on several instances of the grid-world problem.

Learning automataComputer sciencebusiness.industryBootstrappingMachine learningcomputer.software_genreRegressionConvolutionRobustness (computer science)Bellman equationReinforcement learningMarkov decision processArtificial intelligenceMathematics::Representation Theorybusinesscomputer
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Back to the Amitsur-Levitzki theorem: a super version for the orthosymplectic Lie superalgebra osp(1, 2n)

2003

We prove an Amitsur-Levitzki type theorem for the Lie superalgebras osp(1,2n) inspired by Kostant's cohomological interpretation of the classical theorem. We show that the Lie superalgebras gl(p,q) cannot satisfy an Amitsur-Levitzki type super identity if p, q are non zero and conjecture that neither can any other classical simple Lie superalgebra with the exception of osp(1,2n).

Lie superalgebraType (model theory)17B2001 natural sciencesInterpretation (model theory)CombinatoricsIdentity (mathematics)Simple (abstract algebra)Mathematics::Quantum Algebra0103 physical sciencesFOS: Mathematics0101 mathematicsRepresentation Theory (math.RT)Classical theoremMathematics::Representation TheoryMathematical PhysicsPhysicsConjecture[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]010308 nuclear & particles physics010102 general mathematicsMathematics::Rings and AlgebrasStatistical and Nonlinear Physics16. Peace & justice17B56[ MATH.MATH-RT ] Mathematics [math]/Representation Theory [math.RT]17B20; 17B56Mathematics - Representation Theory
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The HOMFLY-PT polynomials of sublinks and the Yokonuma–Hecke algebras

2016

We describe completely the link invariants constructed using Markov traces on the Yokonuma-Hecke algebras in terms of the linking matrix and the HOMFLYPT polynomials of sublinks.

MSC: Primary 57M27: Invariants of knots and 3-manifolds Secondary 20C08: Hecke algebras and their representations 20F36: Braid groups; Artin groups 57M25: Knots and links in $S^3$Pure mathematicsMarkov chainGeneral Mathematics010102 general mathematicsYokonuma-Hecke algebrasGeometric Topology (math.GT)Linking numbers01 natural sciencesMathematics::Geometric TopologyMatrix (mathematics)Mathematics - Geometric TopologyMarkov tracesMathematics::Quantum Algebra[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesMathematics - Quantum AlgebraFOS: MathematicsQuantum Algebra (math.QA)010307 mathematical physics0101 mathematicsRepresentation Theory (math.RT)Link (knot theory)Mathematics - Representation TheoryMathematics
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Real structures on nilpotent orbit closures

2021

We determine the equivariant real structures on nilpotent orbits and the normalizations of their closures for the adjoint action of a complex semisimple algebraic group on its Lie algebra.

Mathematics - Algebraic Geometryreal form14R20 14M17 14P99 11S25 20G20homogeneous spaceMathematics::Rings and Algebrasreal structureGalois cohomology[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]FOS: MathematicsNilpotent orbitMathematics::Representation TheoryAlgebraic Geometry (math.AG)
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Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed

2015

We prove that the bihamiltonian cohomology of a semisimple pencil of Poisson brackets of hydrodynamic type vanishes for almost all degrees. This implies the existence of a full dispersive deformation of a semisimple bihamiltonian structure of hydrodynamic type starting from any infinitesimal deformation.

Mathematics - Differential GeometryFOS: Physical sciencesPoisson distribution01 natural sciencessymbols.namesakePoisson bracketMathematics::Quantum Algebra0103 physical sciencesFOS: Mathematics0101 mathematicsMathematics::Representation TheoryMathematics::Symplectic GeometryMathematical PhysicsPencil (mathematics)MathematicsAlgebra and Number TheoryNonlinear Sciences - Exactly Solvable and Integrable Systems010102 general mathematicsMathematical analysisInfinitesimal deformationMathematical Physics (math-ph)Cohomology[ MATH.MATH-DG ] Mathematics [math]/Differential Geometry [math.DG]Nonlinear Sciences::Exactly Solvable and Integrable SystemsDifferential Geometry (math.DG)[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]symbols010307 mathematical physicsGeometry and TopologyExactly Solvable and Integrable Systems (nlin.SI)Analysis
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On Radon transforms on compact Lie groups

2016

We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to $S^1$ nor to $S^3$. This is true for both smooth functions and distributions. The key ingredients of the proof are finding totally geodesic tori and realizing the Radon transform as a family of symmetric operators indexed by nontrivial homomorphisms from $S^1$.

Mathematics - Differential GeometryPure mathematicsGeodesicGeneral MathematicsGroup Theory (math.GR)inversio-ongelmatsymbols.namesake46F12 44A12 22C05 22E30FOS: MathematicsRepresentation Theory (math.RT)MathematicsRadon transformLie groupsinverse problemsApplied Mathematicsta111Lie groupTorusInverse problemInjective functionFourier analysisDifferential Geometry (math.DG)Fourier analysissymbolsRay transformsHomomorphismMathematics - Group TheoryMathematics - Representation Theory
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