canonical basis

This family is the canonical basis of the R-module (free module)

In the canonical basis of elementary derivations , it is written as:

Once she had been principal, had been demoted on some hazy canonical basis.

(here, is the hyperoctahedral group) and , which means that they describe canonical basis of the double class algebras and .

The Kazhdan-Lusztig polynomials arise as transition coefficients between their canonical basis and the natural basis of the Hecke algebra.

Kazhdan and Lusztig used this to construct a canonical basis in the Hecke algebra of the Coxeter group and its representations.

In mathematics, a canonical basis is a basis of an algebraic structure that is canonical in a sense that depends on the precise context:

The Kazhdan-Lusztig notions of left, right and two-sided cells in Coxeter groups are defined through the behavior of the canonical basis under the action of H.

In mathematics, the standard basis (also called natural basis or canonical basis) for a Euclidean space consists of one unit vector pointing in the direction of each axis of the Cartesian coordinate system.

However such a module is still isomorphic to a quotient of some module R with n finite (to see this it suffices to construct the morphism that sends the elements of the canonical basis R to the generators of the module, and take the quotient by its kernel.)