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・ Affine braid group
・ Affine bundle
・ Affine cipher
・ Affine combination
・ Affine connection
・ Affine coordinate system
・ Affine curvature
・ Affine differential geometry
・ Affine focal set
・ Affine gauge theory
・ Affine geometry
・ Affine geometry of curves
・ Affine Grassmannian
・ Affine Grassmannian (manifold)
・ Affine group
Affine Hecke algebra
・ Affine hull
・ Affine involution
・ Affine Lie algebra
・ Affine logic
・ Affine manifold
・ Affine manifold (disambiguation)
・ Affine monoid
・ Affine plane
・ Affine plane (incidence geometry)
・ Affine pricing
・ Affine q-Krawtchouk polynomials
・ Affine representation
・ Affine root system
・ Affine shape adaptation


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Affine Hecke algebra : ウィキペディア英語版
Affine Hecke algebra
In mathematics, an affine Hecke algebra is the Hecke algebra of an affine Weyl group, and can be used to prove Macdonald's constant term conjecture for Macdonald polynomials.
==Definition==
Let V be a Euclidean space of a finite dimension and \Sigma an affine root system on V. An affine Hecke algebra is a certain associative algebra that deforms the group algebra \mathbb() of the Weyl group W of \Sigma (the affine Weyl group). It is usually denoted by H(\Sigma,q), where q:\Sigma\rightarrow \mathbb is multiplicity function that plays the role of deformation parameter. For q\equiv 1 the affine Hecke algebra H(\Sigma,q) indeed reduces to \mathbb().

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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