46,177 research outputs found
Twisted root system of a (*)-subgroup
We classify (*)-subgroups of compact Lie groups of adjoint type, and
associate a twisted root system to every (*)-subgroup. We study the structure
of twisted root system in several aspects: properties of the small Weyl group
W_{small} and its normal subgroups W_{tiny} and W_{f}; properties of finite
root datum; structure of strips of infinite roots.Comment: 49 pages, no figure. Comments and suggestions are welcom
Elementary abelian 2 subgroups of compact Lie groups
We classify elementary abelian 2 subgroups of compact simple Lie groups of
adjoint type. This finishes the classification of elementary abelian
subgroups of compact (or linear algebraic) simple groups of adjoint type.Comment: 40 pages, comments are welcom
Maximal abelian subgroups of compact simple Lie groups of type E
We classify closed abelian subgroups of a compact simple Lie group of adjoint
type and of type E having centralizer of the same dimension as the dimension of
the subgroup and describe Weyl groups of maximal abelian subgroups.Comment: Together another two papers, this paper replaces arXiv:1211.1334 and
also completes arguments in i
Acceptable compact Lie groups
In this paper we show that for a connected compact Lie group to be acceptable
it is necessary and sufficient that its derived subgroup is isomorphic to a
direct product of the groups , , , , . We
also study pseudo-characters for the group
Maximal abelian subgroups of compact matrix groups
We classify closed abelian subgroups of the automorphism group of any compact
classical simple Lie algebra whose centralizer has the same dimension as the
dimension of the subgroup, and describe Weyl groups of maximal abelian
subgroups.Comment: arXiv admin note: substantial text overlap with arXiv:1211.133
Maximal abelian subgroups of Spin groups and some exceptional simple Lie groups
We classify closed abelian subgroups of the simple groups , ,
having centralizer the same dimension as the dimension of the
subgroup, as well as finite abelian subgroups of certain spin and half-spin
groups having finite centralizer.Comment: arXiv admin note: text overlap with arXiv:1211.133
A note on closed subgroups of compact Lie groups
We reduce the classification of finite subgroups in compact Lie groups to
that of quasi-simple ones, prove the number of conjugacy classes is finite and
each cojugacy class is Zariski closed in mapping space, and classify "strongly
controlling fusions" symmetric pairs.Comment: v3, 17 page
A rigidity result for dimension data
The dimension datum of a closed subgroup of a compact Lie group is a sequence
by assigning the invariant dimension of each irreducible representation
restricting to the subgroup. We prove that any sequence of dimension data
contains a converging sequence with limit the dimension datum of a subgroup
interrelated to subgroups giving this sequence. This rigidity has an immediate
corollary that the space of dimension data of closed subgroups in a given
compact Lie group is sequentially compact
Cross-modal Subspace Learning via Kernel Correlation Maximization and Discriminative Structure Preserving
The measure between heterogeneous data is still an open problem. Many
research works have been developed to learn a common subspace where the
similarity between different modalities can be calculated directly. However,
most of existing works focus on learning a latent subspace but the semantically
structural information is not well preserved. Thus, these approaches cannot get
desired results. In this paper, we propose a novel framework, termed
Cross-modal subspace learning via Kernel correlation maximization and
Discriminative structure-preserving (CKD), to solve this problem in two
aspects. Firstly, we construct a shared semantic graph to make each modality
data preserve the neighbor relationship semantically. Secondly, we introduce
the Hilbert-Schmidt Independence Criteria (HSIC) to ensure the consistency
between feature-similarity and semantic-similarity of samples. Our model not
only considers the inter-modality correlation by maximizing the kernel
correlation but also preserves the semantically structural information within
each modality. The extensive experiments are performed to evaluate the proposed
framework on the three public datasets. The experimental results demonstrated
that the proposed CKD is competitive compared with the classic subspace
learning methods.Comment: The paper is under consideration at Multimedia Tools and Application
Unsupervised Multi-modal Hashing for Cross-modal retrieval
With the advantage of low storage cost and high efficiency, hashing learning
has received much attention in the domain of Big Data. In this paper, we
propose a novel unsupervised hashing learning method to cope with this open
problem to directly preserve the manifold structure by hashing. To address this
problem, both the semantic correlation in textual space and the locally
geometric structure in the visual space are explored simultaneously in our
framework. Besides, the `2;1-norm constraint is imposed on the projection
matrices to learn the discriminative hash function for each modality. Extensive
experiments are performed to evaluate the proposed method on the three publicly
available datasets and the experimental results show that our method can
achieve superior performance over the state-of-the-art methods.Comment: 4 pages, 4 figure
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