Duality and deformations of stable Grothendieck polynomials
Duality and deformations of stable Grothendieck polynomials
复制标题
稳定格洛腾迪克多项式的对偶性和变形
DOI：
10.1007/s10801-016-0708-4
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发表时间：
2016
影响因子：
0.8
通讯作者：
Damir Yeliussizov
中科院分区：
文献类型：
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作者：
Damir Yeliussizov
稳定的Grothendieck多项式可以看作是Schur多项式的K-理论模拟。我们将稳定的Grothendieck多项式推广到两参数形式，我们称之为规范稳定的Grothendieck函数。这些函数具有与稳定的Grothendieck多项式相同的结构常数(具有标度)，并且在标准对合环自同构下是自对偶的(与参数切换合成)。我们研究了这些函数的各种性质，包括组合公式、Schur展开式、Jacobi-Trudi型恒等式和相关的Fomin-Greene算子。
Stable Grothendieck polynomials can be viewed as a K-theory analog of Schur polynomials. We extend stable Grothendieck polynomials to a two-parameter version, which we call canonical stable Grothendieck functions. These functions have the same structure constants (with scaling) as stable Grothendieck polynomials and (composing with parameter switching) are self-dual under the standard involutive ring automorphism. We study various properties of these functions, including combinatorial formulas, Schur expansions, Jacobi–Trudi-type identities, and associated Fomin–Greene operators.