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arXiv · 1207.2216

Equivariant Cohomology of Weighted Grassmannians and Weighted Schubert Classes

Hiraku Abe·Tomoo Matsumura
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Abstract

In this paper, we study the T_w-equivariant cohomology of the weighted Grassmannians wGr(d,n) introduced by Corti-Reid where T_w is the n-dimensional torus that naturally acts on wGr(d,n). We introduce the equivariant weighted Schubert classes and, after we show that they form a basis of the equivariant cohomology, we give an explicit formula for the structure constants with respect to this Schubert basis. We also find a linearly independent subset {wu_1,...,wu_n} of Lie(T_w)^* such that those structure constants are polynomials in wu_i's with non-negative coefficients, up to a permutation on the weights.

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BibTeXRIS

Hiraku Abe, Tomoo Matsumura. 2013-10-29. Equivariant Cohomology of Weighted Grassmannians and Weighted Schubert Classes. https://arxiv.org/abs/1207.2216

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