Let F:R4n→R4n be an element of the quaternionic unitary group Sp(n) · Sp(1), let K be a compact subset of R4n, and let V be a 4. k-dimensional quaternionic subspace of R4n≅Hn. The 4. k-dimensional shadow of the image under F of K is its orthogonal projection P(F(K)) onto V. We show that there exists a 4. k-dimensional quaternionic subspace W of R4n such that the volume of the shadow P(F(K)) is the same as the volume of the section K∩. W. This is a quaternionic analogue of the symplectic linear non-squeezing result recently obtained by Abbondandolo and Matveyev.
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Titolo: | On the volume of the Sp(n)·Sp(1) shadow of a compact set |
Autori: | |
Data di pubblicazione: | 2016 |
Rivista: | |
Handle: | http://hdl.handle.net/11586/265121 |
Appare nelle tipologie: | 1.1 Articolo in rivista |