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Infinite-dimensional p-adic groups, semigroups of double cosets, and inner functions on Bruhat–Tits buildingsстатья
Информация о цитировании статьи получена из
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Дата последнего поиска статьи во внешних источниках: 20 ноября 2019 г.
- Автор: Neretin Yu A.
- Журнал: Izvestiya. Mathematics
- Том: 79
- Номер: 3
- Год издания: 2015
- Издательство: American Mathematical Society
- Местоположение издательства: United States
- Первая страница: 512
- Последняя страница: 553
- DOI: 10.1070/IM2015v079n03ABEH002752
- Аннотация: We construct $p$-adic analogues of operator colligations and their characteristic functions. Consider a $p$-adic group $G=GL(\alpha+k\infty,\mathbb{Q}_p)$, a subgroup $L=O(k\infty,\mathb{Z}_p) of $G$ and a subgroup $K=O(\infty),\mathbb{Q}_p)$ which is diagonally embedded in $L$. We show that the space $\Gamma=K∖G/K$ of double cosets admits the structure of a semigroup and acts naturally on the space of $K$-fixed vectors of any unitary representation of $G$. With each double coset we associate a ‘characteristic function’ that sends a certain Bruhat–Tits building to another building (the buildings are finite-dimensional) in such a way that the image of the distinguished boundary lies in the distinguished boundary. The second building admits the structure of a (Nazarov) semigroup, and the product in $\Gamma$ corresponds to the pointwise product of characteristic functions.
- Добавил в систему: Неретин Юрий Александрович