104 research outputs found
Cycle Connectivity and Automorphism Groups of Flag Domains
A flag domain is an open orbit of a real form in a flag manifold
of its complexification. If is holomorphically convex, then, since
it is a product of a Hermitian symmetric space of bounded type and a compact
flag manifold, is easily described. If is not holomorphically
convex, then in our previous work (American J. Math, 136, Nr.2 (2013) 291-310
(arXiv: 1003.5974)) it was shown that is a Lie group whose connected
component at the identity agrees with except possibly in situations which
arise in Onishchik's list of flag manifolds where is larger than
. These exceptions are handled in detail here. In addition substantially
simpler proofs of some of our previous work are given.Comment: To appear in Birkh\"auser Progress Reports "Current Developments and
Retrospectives in Lie Theor
On hyperbolicity of SU(2)-equivariant, punctured disc bundles over the complex affine quadric
Given a holomorphic line bundle over the complex affine quadric , we
investigate its Stein, SU(2)-equivariant disc bundles. Up to equivariant
biholomorphism, these are all contained in a maximal one, say .
By removing the zero section to one obtains the unique Stein,
SU(2)-equivariant, punctured disc bundle over which contains entire
curves. All other such punctured disc bundles are shown to be Kobayashi
hyperbolic.Comment: 15 pages, v2: minor changes, to appear in Transformation Group
Symmetry classes of disordered fermions
Building upon Dyson's fundamental 1962 article known in random-matrix theory
as 'the threefold way', we classify disordered fermion systems with quadratic
Hamiltonians by their unitary and antiunitary symmetries. Important examples
are afforded by noninteracting quasiparticles in disordered metals and
superconductors, and by relativistic fermions in random gauge field
backgrounds.
The primary data of the classification are a Nambu space of fermionic field
operators which carry a representation of some symmetry group. Our approach is
to eliminate all of the unitary symmetries from the picture by transferring to
an irreducible block of equivariant homomorphisms. After reduction, the block
data specifying a linear space of symmetry-compatible Hamiltonians consist of a
basic vector space V, a space of endomorphisms in End(V+V*), a bilinear form on
V+V* which is either symmetric or alternating, and one or two antiunitary
symmetries that may mix V with V*. Every such set of block data is shown to
determine an irreducible classical compact symmetric space. Conversely, every
irreducible classical compact symmetric space occurs in this way.
This proves the correspondence between symmetry classes and symmetric spaces
conjectured some time ago.Comment: 52 pages, dedicated to Freeman J. Dyson on the occasion of his 80th
birthda
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