Orthogonal polynomials | Discrete groups | Lie algebras

Affine root system

In mathematics, an affine root system is a root system of affine-linear functions on a Euclidean space. They are used in the classification of affine Lie algebras and superalgebras, and semisimple p-adic algebraic groups, and correspond to families of Macdonald polynomials. The reduced affine root systems were used by Kac and Moody in their work on Kac–Moody algebras. Possibly non-reduced affine root systems were introduced and classified by and (except that both these papers accidentally omitted the Dynkin diagram ). (Wikipedia).

Affine root system
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From playlist Quadratic Systems

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From playlist Parabolas

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More resources available at www.misterwootube.com

From playlist Using Complex Numbers

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From playlist Eigenvalues

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From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

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From playlist Applied Cryptography

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From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory

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From playlist Quadratic Systems

Related pages

Kac–Moody algebra | Dynkin diagram | Affine space | Algebraic group | Macdonald polynomials | Root system | Lie superalgebra | Macdonald identities | Euclidean space | Lie algebra