nLab
fundamental representation
Contents
Context
Representation theory
representation theory
geometric representation theory
Ingredients
representation, 2-representation, ∞-representation
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group, ∞-group
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group algebra, algebraic group, Lie algebra
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vector space, n-vector space
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affine space, symplectic vector space
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action, ∞-action
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module, equivariant object
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bimodule, Morita equivalence
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induced representation, Frobenius reciprocity
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Hilbert space, Banach space, Fourier transform, functional analysis
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orbit, coadjoint orbit, Killing form
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unitary representation
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geometric quantization, coherent state
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socle, quiver
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module algebra, comodule algebra, Hopf action, measuring
Geometric representation theory
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D-module, perverse sheaf,
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Grothendieck group, lambda-ring, symmetric function, formal group
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principal bundle, torsor, vector bundle, Atiyah Lie algebroid
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geometric function theory, groupoidification
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Eilenberg-Moore category, algebra over an operad, actegory, crossed module
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reconstruction theorems
Contents
Idea
A finite dimensional irreducible representation of a semisimple Lie group or Lie algebra is called the fundamental representation if its highest weight is a fundamental weight?.
References
See also:
Last revised on May 18, 2022 at 14:12:35.
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