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 $p$ 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 $SU(n)$, $Sp(n)$, $SO(2n+1)$, $G_2$, $SO(4)$. We also study pseudo-characters for the group $SO_{4}(\mathbb{C})$

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 $G_2$, $F_4$, $Aut(so(8))$ 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

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

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