|
Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
Isometric Embeddings of Infinite-dimensional Grassmannians
Emma Previatoa, Mauro Sperab a Department of Mathematics and Statistics, Boston University, Boston, MA 02215-2411, USA
b Dipartimento di Informatica, Università degli Studi di Verona, 37134 Verona, Italy
Аннотация:
We investigate geometric properties of the (Sato–Segal–Wilson)
Grassmannian and its submanifolds, with special attention to the orbits of
the KP flows. We use a coherent-states model, by which Spera and
Wurzbacher gave equations for the image of a product of Grassmannians
using the Powers–Størmer purification procedure. We extend to this
product Sato's idea of turning equations that define the projective
embedding of a homogeneous space into a hierarchy of partial differential
equations. We recover the BKP equations from the classical Segre embedding
by specializing the equations to finite-dimensional
submanifolds.
We revisit the calculation of Calabi's
diastasis function given by Spera and Valli again in the context of
$C^\ast$-algebras, using the $\tau$-function to give an expression of the
diastasis on the infinite-dimensional Grassmannian; this expression can be
applied to the image of the Krichever map to give a proof of Weil's
reciprocity based on the fact that the distance of two points on the
Grassmannian is symmetric. Another application is the fact that each
(isometric) automorphism of the Grassmannian is induced by a projective
transformation in the Plücker embedding.
Ключевые слова:
Calabi’s diastasis function, Canonical Anticommutation Relations, Universal Grassmann Manifold, Weil reciprocity, $\tau$-function.
Поступила в редакцию: 09.05.2010 Принята в печать: 01.02.2011
Образец цитирования:
Emma Previato, Mauro Spera, “Isometric Embeddings of Infinite-dimensional Grassmannians”, Regul. Chaotic Dyn., 16:3-4 (2011), 356–373
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd442 https://www.mathnet.ru/rus/rcd/v16/i3/p356
|
Статистика просмотров: |
Страница аннотации: | 81 |
|