759,277 research outputs found

### Multiplicity one theorems: the Archimedean case

Let $G$ be one of the classical Lie groups \GL_{n+1}(\R), \GL_{n+1}(\C),
\oU(p,q+1), \oO(p,q+1), \oO_{n+1}(\C), \SO(p,q+1), \SO_{n+1}(\C), and
let $G'$ be respectively the subgroup \GL_{n}(\R), \GL_{n}(\C), \oU(p,q),
\oO(p,q), \oO_n(\C), \SO(p,q), \SO_n(\C), embedded in $G$ in the
standard way. We show that every irreducible Casselman-Wallach representation
of $G'$ occurs with multiplicity at most one in every irreducible
Casselman-Wallach representation of $G$. Similar results are proved for the
Jacobi groups \GL_{n}(\R)\ltimes \oH_{2n+1}(\R), \GL_{n}(\C)\ltimes
\oH_{2n+1}(\C), \oU(p,q)\ltimes \oH_{2p+2q+1}(\R), \Sp_{2n}(\R)\ltimes
\oH_{2n+1}(\R), \Sp_{2n}(\C)\ltimes \oH_{2n+1}(\C), with their respective
subgroups \GL_{n}(\R), \GL_{n}(\C), \oU(p,q), \Sp_{2n}(\R),
\Sp_{2n}(\C).Comment: To appear in Annals of Mathematic

### The theory of magnetic field induced domain-wall propagation in magnetic nanowires

A global picture of magnetic domain wall (DW) propagation in a nanowire
driven by a magnetic field is obtained: A static DW cannot exist in a
homogeneous magnetic nanowire when an external magnetic field is applied. Thus,
a DW must vary with time under a static magnetic field. A moving DW must
dissipate energy due to the Gilbert damping. As a result, the wire has to
release its Zeeman energy through the DW propagation along the field direction.
The DW propagation speed is proportional to the energy dissipation rate that is
determined by the DW structure. An oscillatory DW motion, either the precession
around the wire axis or the breath of DW width, should lead to the speed
oscillation.Comment: 4 pages, 2 figure

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