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arXiv · 0712.2580

Extended quadratic algebra and a model of the equivariant cohomology ring of flag varieties

Anatol N. Kirillov·Toshiaki Maeno
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Abstract

For the 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 of our construction we describe a generalization of the equivariant Pieri rule for double Schubert polynomials. For a general finite Coxeter system we construct an extension of the corresponding Nichols-Woronowicz algebra. In the case of finite crystallographic Coxeter systems we present a construction of extended Nichols-Woronowicz algebra model for the equivariant cohomology of the corresponding flag variety.

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Anatol N. Kirillov, Toshiaki Maeno. 2008-11-10. Extended quadratic algebra and a model of the equivariant cohomology ring of flag varieties. https://arxiv.org/abs/0712.2580

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