Invariant Functions on Grassmannians
| dc.creator | Ólafsson, Gestur | |
| dc.creator | Rubin, Boris | |
| dc.date | 2007-12-29 | |
| dc.date.accessioned | 2026-07-07T08:51:54Z | |
| dc.date.available | 2026-07-07T08:51:54Z | |
| dc.description | It is known, that every function on the unit sphere in $\bbr^n$, which is invariant under rotations about some coordinate axis, is completely determined by a function of one variable. Similar results, when invariance of a function reduces dimension of its actual argument, hold for every compact symmetric space and can be obtained in the framework of Lie-theoretic consideration. In the present article, this phenomenon is given precise meaning for functions on the Grassmann manifold $G_{n,i}$ of $i$-dimensional subspaces of $\bbr^n$, which are invariant under orthogonal transformations preserving complementary coordinate subspaces of arbitrary fixed dimension. The corresponding integral formulas are obtained. Our method relies on bi-Stiefel decomposition and does not invoke Lie theory. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/0801.0081 | |
| dc.identifier | http://arxiv.org/abs/0801.0081 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145099 | |
| dc.subject | Functional Analysis | |
| dc.subject | 44A12; 52A38 | |
| dc.title | Invariant Functions on Grassmannians | |
| dc.type | text |