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Symmetric shift-invariant subspaces and harmonic maps

Aleman, Alexandru LU ; Pacheco, Rui and Wood, John C. (2021) In Mathematische Zeitschrift 299(1-2). p.183-202
Abstract

The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an important class of harmonic maps into symmetric and k-symmetric spaces. Using an appropriate description of such symmetric shift-invariant subspaces we obtain new results for the corresponding extended solutions, including how to obtain primitive harmonic maps from certain harmonic maps into the unitary group.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Flag manifolds, Harmonic maps, Primitive maps, Riemann surfaces, Shift-invariant subspaces
in
Mathematische Zeitschrift
volume
299
issue
1-2
pages
20 pages
publisher
Springer
external identifiers
  • scopus:85114826133
ISSN
0025-5874
DOI
10.1007/s00209-020-02680-9
language
English
LU publication?
yes
id
c21e2b35-fed5-4edc-b613-369085f846b8
date added to LUP
2021-10-08 14:09:11
date last changed
2022-04-27 04:32:16
@article{c21e2b35-fed5-4edc-b613-369085f846b8,
  abstract     = {{<p>The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an important class of harmonic maps into symmetric and k-symmetric spaces. Using an appropriate description of such symmetric shift-invariant subspaces we obtain new results for the corresponding extended solutions, including how to obtain primitive harmonic maps from certain harmonic maps into the unitary group.</p>}},
  author       = {{Aleman, Alexandru and Pacheco, Rui and Wood, John C.}},
  issn         = {{0025-5874}},
  keywords     = {{Flag manifolds; Harmonic maps; Primitive maps; Riemann surfaces; Shift-invariant subspaces}},
  language     = {{eng}},
  number       = {{1-2}},
  pages        = {{183--202}},
  publisher    = {{Springer}},
  series       = {{Mathematische Zeitschrift}},
  title        = {{Symmetric shift-invariant subspaces and harmonic maps}},
  url          = {{http://dx.doi.org/10.1007/s00209-020-02680-9}},
  doi          = {{10.1007/s00209-020-02680-9}},
  volume       = {{299}},
  year         = {{2021}},
}