标题： Toda型对部分旗形流形的量子K理论的表示 显示英文标题

标题： Toda-type presentations for the quantum K theory of partial flag varieties

摘要： 我们证明了偏旗簇 $\mathrm{Fl}(r_1, \ldots, r_k;n)$的等变 K 理论的一个行列式、Toda 类型的表示。 证明依赖于通过 Kato 从 $\mathrm{Fl}(n)$的量子 K 环到 $\mathrm{Fl}(r_1, \ldots, r_k;n)$的 $\mathrm{K}_T(\mathrm{pt})$-代数同态，将 Maeno、Naito 和 Sagaki 对完全旗簇 $\mathrm{Fl}(n)$得到的 Toda 表示向前推。 从 $\mathrm{Fl}(n)$的 Whitney 表示出发，我们证明同样的前推技术给出了任意偏旗簇中不依赖于量子参数的量子 K Schubert 类的多项式表示的递归公式。 在附录中，我们包含对等变量子K环的Toda表示的另一个证明，针对$\mathrm{Fl}(n)$，这是遵循Anderson、Chen和Tseng的方法，该方法基于量子理论中的$\mathrm{K}$$J$-函数是有限差分Toda哈密顿量的本征函数这一事实。 显示英文摘要

摘要： We prove a determinantal, Toda-type, presentation for the equivariant K theory of a partial flag variety $\mathrm{Fl}(r_1, \ldots, r_k;n)$. The proof relies on pushing forward the Toda presentation obtained by Maeno, Naito and Sagaki for the complete flag variety $\mathrm{Fl}(n)$, via Kato's $\mathrm{K}_T(\mathrm{pt})$-algebra homomorphism from the quantum K ring of $\mathrm{Fl}(n)$ to that of $\mathrm{Fl}(r_1, \ldots, r_k;n)$. Starting instead from the Whitney presentation for $\mathrm{Fl}(n)$, we show that the same push-forward technique gives a recursive formula for polynomial representatives of quantum K Schubert classes in any partial flag variety which do not depend on quantum parameters. In an appendix, we include another proof of the Toda presentation for the equivariant quantum K ring of $\mathrm{Fl}(n)$, following Anderson, Chen, and Tseng, which is based on the fact that the $\mathrm{K}$ theoretic $J$-function is an eigenfunction of the finite difference Toda Hamiltonians.