某些准分裂型修正$$\imath $$量子群的晶体基

Pub Date : 2023-06-14 DOI:10.1007/s10468-023-10207-z

Hideya Watanabe

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引用次数: 0

摘要

为了看清在（q = \infty）处的（（（imath））规范基的行为，我们引入了与（（imath））量子群的某种准分裂类型相关联的（（imath））晶体的概念。$\imath$晶体的理论阐明了为什么$\imath$规范基元在自然同态下并不总是保留的。同时，我们构造了一个投影系统的（（imath）晶体），它的投影极限可以被认为是在（q = \infty \）处的修正量子群的（（imath）规范基础）。

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Crystal Bases of Modified $\imath $quantum Groups of Certain Quasi-Split Types

In order to see the behavior of $\imath $canonical bases at $q = \infty $, we introduce the notion of $\imath $crystals associated to an $\imath $quantum group of certain quasi-split type. The theory of $\imath $crystals clarifies why $\imath $canonical basis elements are not always preserved under natural homomorphisms. Also, we construct a projective system of $\imath $crystals whose projective limit can be thought of as the $\imath $canonical basis of the modified $\imath $quantum group at $q = \infty $.

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