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摘要翻译：
本文证明了旗簇G/P的T-等变K-理论K_T(G/P)的一些一般结果，其中G是半单复代数群，P是抛物子群，T$是P中包含的极大环面。特别地，我们对K_T(G/P)中由Schubert变体的结构束的对偶给出的K_T(G/P)的基写成的两个基元的乘积在K_T(G/P)中的正性现象作了猜想。（对于全旗品种G/B，这个对偶基与Kostant-Kumar给出的基密切相关。）该猜想与Griffeth-Ram关于结构束基中乘积的结构常数的猜想平行（但不同）。利用这些基给出了射影空间T-等变K-理论中乘积的显式表达式。特别地，我们在这种情况下建立了我们的猜想和Griffeth-Ram猜想。
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英文标题：
《On positivity in T-equivariant K-theory of flag varieties》
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作者：
William Graham, Shrawan Kumar
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Representation Theory 表象理论
分类描述：Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
代数和群的线性表示，李理论，结合代数，多重线性代数
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英文摘要：
We prove some general results on the T-equivariant K-theory K_T(G/P) of the flag variety G/P, where G is a semisimple complex algebraic group, P is a parabolic subgroup and T$ is a maximal torus contained in P. In particular, we make a conjecture about a positivity phenomenon in K_T(G/P) for the product of two basis elements written in terms of the basis of K_T(G/P) given by the dual of the structure sheaf (of Schubert varieties) basis. (For the full flag variety G/B, this dual basis is closely related to the basis given by Kostant-Kumar.) This conjecture is parallel to (but different from) the conjecture of Griffeth-Ram for the structure constants of the product in the structure sheaf basis. We give explicit expressions for the product in the T-equivariant K-theory of projective spaces in terms of these bases. In particular, we establish our conjecture and the conjecture of Griffeth-Ram in this case.
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PDF链接：
https://arxiv.org/pdf/0801.2776
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