论文标题
均值$ k $ - 半灭旗歧管的理论作为nil-daha模块
Equivariant $K$-theory of the semi-infinite flag manifold as a nil-DAHA module
论文作者
论文摘要
高度$ k $ - 由Kato，Naito和Sagaki最近开发的Semi-Infinite Flag歧管的理论，采用了NIL-Double Affine Hecke Algebra（Nil-Daha）和$ Q $ -Heisenberg Algebra的通勤动作。后者的动作产生了一个免费的等级$ | w | $的子模块，其中$ w $是（有限的）Weyl组。我们表明，在尼尔达哈（Nil-Daha）下，该子模块是稳定的，这使人们能够以$ w \ times w $矩阵在$ q $ -Heisenberg代数上表达Nil-Daha动作。我们的主要结果使这些矩阵的明确代数结构是（非nil）Daha的限制，以简单的类型。这种构造表明，当用赫里贝格代数表示时，乘以繁殖是由Cherednik和作者引入的非对称$ Q $ -TODA系统给出的。
The equivariant $K$-theory of the semi-infinite flag manifold, as developed recently by Kato, Naito, and Sagaki, carries commuting actions of the nil-double affine Hecke algebra (nil-DAHA) and a $q$-Heisenberg algebra. The action of the latter generates a free submodule of rank $|W|$, where $W$ is the (finite) Weyl group. We show that this submodule is stable under the nil-DAHA, which enables one to express the nil-DAHA action in terms of $W\times W$ matrices over the $q$-Heisenberg algebra. Our main result gives an explicit algebraic construction of these matrices as a limit from the (non-nil) DAHA in simply-laced type. This construction reveals that multiplication by equivariant scalars, when expressed in terms of the Heisenberg algebra, is given by the nonsymmetric $q$-Toda system introduced by Cherednik and the author.
