Recall the classical result that the cup product structure constants for the singular cohomology with integral coefficients H*(G(r)(r, n)) of the Grassmannian of r-planes coincide with the Littlewood-Richardson tensor product structure constants for GL(r). Specifically, the result asserts that there is an explicit surjective ring homomorphism. : Reppoly(GLr). H*(Gr(r, n)), where Gr(r, n) denotes the Grassmannian of r-planes in Cn and Reppoly(GL(r)) denotes the polynomial representation ring of GL(r). This work seeks to achieve one possible generalization of this classical result for GL(r) and the Grassmannian G(r)(r, n) to the Levi subgroups of any reductive group G and the corresponding flag varieties.
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机译：回想一下经典结果，r平面的格拉斯曼ian积分系数H *（G（r）（r，n））的奇同调的杯子积结构常数与GL（的Littlewood-Richardson张量积结构常数一致） r）。具体而言，该结果断言存在显式的排斥环同态。 ：Reppoly（GLr）。 H *（Gr（r，n）），其中Gr（r，n）表示Cn中r平面的Grassmannian，Reppoly（GL（r））表示GL（r）的多项式表示环。这项工作寻求对GL（r）和Grassmannian G（r）（r，n）的经典结果到任何归约组G的Levi子组和相应的标志变体进行一种可能的推广。
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