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Parabolic induction information


In mathematics, parabolic induction is a method of constructing representations of a reductive group from representations of its parabolic subgroups.

If G is a reductive algebraic group and is the Langlands decomposition of a parabolic subgroup P, then parabolic induction consists of taking a representation of , extending it to P by letting N act trivially, and inducing the result from P to G.

There are some generalizations of parabolic induction using cohomology, such as cohomological parabolic induction and Deligne–Lusztig theory.

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Parabolic induction

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mathematics, parabolic induction is a method of constructing representations of a reductive group from representations of its parabolic subgroups. If...

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Induction

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Strong induction Structural induction Transfinite induction Epsilon-induction Parabolic induction Inductive reasoning, in logic Electromagnetic induction Electrostatic...

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Parabolic

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function Parabolic induction Parabolic Lie algebra Parabolic partial differential equation In physics: Parabolic trajectory In technology: Parabolic antenna...

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Zuckerman functor

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groups, ISBN 3-7643-3037-6 Anthony W. Knapp, David A. Vogan, Cohomological induction and unitary representations, ISBN 0-691-03756-6 prefacereview by Dan BarbaschMR1330919...

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Induced representation

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induction construction can be formulated in terms of systems of imprimitivity. In Lie theory, an extremely important example is parabolic induction:...

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Langlands decomposition

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subgroup A, and a nilpotent subgroup N. A key application is in parabolic induction, which leads to the Langlands program: if G {\displaystyle G} is...

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Representation theory of finite groups

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{\displaystyle S_{n}} ; the above-mentioned induction process gets replaced by so-called parabolic induction. However, unlike for S n {\displaystyle S_{n}}...

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Induction lamp

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The induction lamp, electrodeless lamp, or electrodeless induction lamp is a gas-discharge lamp in which an electric or magnetic field transfers the power...

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Parabolic aluminized reflector

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A parabolic aluminized reflector lamp (PAR lamp or simply PAR) is a type of electric lamp that is widely used in commercial, residential, and transportation...

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Linear algebraic group

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decomposition, BN pair, Weyl group, Cartan subgroup, group of adjoint type, parabolic induction Real form (Lie theory), Satake diagram Adelic algebraic group, Weil's...

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Discrete series representation

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series representations can also be constructed by cohomological parabolic induction using Zuckerman functors. Blattner's conjecture Holomorphic discrete...

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Unipotent representation

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groups by some sort of systematic process, such as (cohomological or parabolic) induction. Over finite fields, the unipotent representations are those that...

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Inductively coupled plasma mass spectrometry

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is Varian patented used by Analytik Jena ICP-MS 90 degrees reflecting parabolic "Ion Mirror" optics, which are claimed to provide more efficient ion transport...

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Searchlight

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extremely bright source (traditionally a carbon arc lamp) with a mirrored parabolic reflector to project a powerful beam of light of approximately parallel...

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Heinrich Hertz

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this, Hertz thought it was too difficult, and worked on electromagnetic induction instead. Hertz did produce an analysis of Maxwell's equations during his...

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Eye

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reduced resolution. In the parabolic superposition compound eye type, seen in arthropods such as mayflies, the parabolic surfaces of the inside of each...

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Electromagnetic interference

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external source that affects an electrical circuit by electromagnetic induction, electrostatic coupling, or conduction. The disturbance may degrade the...

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Mechanically powered flashlight

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the handle to its original position after each engagement. The linear induction, Faraday flashlight, or "shake flashlight" is another type of mechanically...

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Wireless power transfer

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charging handheld devices like phones and electric toothbrushes, RFID tags, induction cooking, and wirelessly charging or continuous wireless power transfer...

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Edison light bulb

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generation Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR) Aviation obstruction Balanced-arm lamp Chandelier...

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Copper in renewable energy

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rays in an absorber tube similar to parabolic trough plants. Since the concentration factor is less than in parabolic trough plants, the temperature of...

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Invention of radio

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attempted to build systems based on electric conduction, electromagnetic induction, or on other theoretical ideas. Several inventors/experimenters came across...

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Lens antenna

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have analogues in microwave lenses. Lens antennas have similarities to parabolic antennas and are used in similar applications. In both, microwaves emitted...

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