Geodesic
Extended quadratic algebra and a~model of the equivariant cohomology ring of flag varieties
Algebra i analiz, Tome 22 (2010) no. 3, pp. 155-176.

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For a root system of type $A$, we introduce and study a certain extension of the quadratic algebra invented by S. Fomin and the first author, to construct a model for the equivariant cohomology ring of the corresponding flag variety. As an application, a generalization of the equivariant Pieri rule for double Schubert polynomials is described. For a general finite Coxeter system, an extension of the corresponding Nichols–Woronowicz algebra is constructed. In the case of finite crystallographic Coxeter systems, a construction is presented of an extended Nichols–Woronowicz algebra model for the equivariant cohomology of the corresponding flag variety.
Keywords: root system of type $A$, equivariant Pieri rule, Nichols–Woronowicz algebra. 
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A. N. Kirillov; T. Maeno. Extended quadratic algebra and a~model of the equivariant cohomology ring of flag varieties. Algebra i analiz, Tome 22 (2010) no. 3, pp. 155-176. http://geodesic.mathdoc.fr/item/AA_2010_22_3_a7/

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