Elliptic and K-theoretic stable envelopes and Newton polytopes
Elliptic and K-theoretic stable envelopes and Newton polytopes
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椭圆和 K 理论稳定包络线和牛顿多面体
DOI：
10.1007/s00029-019-0451-5
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Varchenko, A.
中科院分区：
文献类型：
--
作者：
Rimányi, R.;Tarasov, V.;Varchenko, A.
本文考虑部分旗簇的余切丛。我们构造了它们的理论稳定包络，并定义了一种椭圆稳定包络。我们期望我们的椭圆稳定包络与M. Aganagic和A. Okounkov.给出了理论稳定包络和椭圆稳定包络的计算公式。我们证明了理论稳定包络是我们的椭圆稳定包络的合适极限。这一现象是M. Aganagic和A. Okounkov.我们的稳定包络线是根据二十年前qKZ方程解的积分表示理论中提出的椭圆权函数和三角权函数构造的。(More准确地说，椭圆权函数只在这种情况下出现过。）我们证明了三角权函数的新性质。也就是说，我们考虑三角权重函数的某些评估，这些评估是多变量洛朗多项式，并表明评估的牛顿多面体嵌入在相应对角评估的牛顿多面体中。该性质意味着三角权函数投影到理论稳定包络线上的事实。
In this paper we consider the cotangent bundles of partial flag varieties. We construct the-theoretic stable envelopes for them and also define a version of the elliptic stable envelopes. We expect that our elliptic stable envelopes coincide with the elliptic stable envelopes defined by M. Aganagic and A. Okounkov. We give formulas for the-theoretic stable envelopes and our elliptic stable envelopes. We show that the-theoretic stable envelopes are suitable limits of our elliptic stable envelopes. That phenomenon was predicted by M. Aganagic and A. Okounkov. Our stable envelopes are constructed in terms of the elliptic and trigonometric weight functions which originally appeared in the theory of integral representations of solutions ofqKZequations twenty years ago. (More precisely, the elliptic weight functions had appeared earlier only for thecase.) We prove new properties of the trigonometric weight functions. Namely, we consider certain evaluations of the trigonometric weight functions, which are multivariable Laurent polynomials, and show that the Newton polytopes of the evaluations are embedded in the Newton polytopes of the corresponding diagonal evaluations. That property implies the fact that the trigonometric weight functions project to the-theoretic stable envelopes.
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DOI：
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发表时间：
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期刊：
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影响因子：
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