Английская Википедия:Holomorphic discrete series representation

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Версия от 13:03, 22 марта 2024; EducationBot (обсуждение | вклад) (Новая страница: «{{Английская Википедия/Панель перехода}} {{Use American English|date = March 2019}} {{Short description|Representation of semisimple Lie groups}} In mathematics, a '''holomorphic discrete series representation''' is a discrete series representation of a semisimple Lie group that can be represented in a natural way as a Hilbert space of holomorphic functions. The simple Lie groups with holomorphic discrete seri...»)
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Шаблон:Use American English Шаблон:Short description In mathematics, a holomorphic discrete series representation is a discrete series representation of a semisimple Lie group that can be represented in a natural way as a Hilbert space of holomorphic functions. The simple Lie groups with holomorphic discrete series are those whose symmetric space is Hermitian. Holomorphic discrete series representations are the easiest discrete series representations to study because they have highest or lowest weights, which makes their behavior similar to that of finite-dimensional representations of compact Lie groups.

Шаблон:Harvtxt found the first examples of holomorphic discrete series representations, and Шаблон:Harvs classified them for all semisimple Lie groups.

Шаблон:Harvtxt and Шаблон:Harvtxt described the characters of holomorphic discrete series representations.

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