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Chemical Research in Chinese Universities 2004年第2期20卷 166-175页

作者： LIAn-yong SchoolofChemistryandChemicalEngineering SouthwesternNormalUniversityChongqing400715P.R.China

A new method based on angular momentum theory was proposed to construct the basis functions of the irreducible representations(IRs) of point groups. The transformation coefficients, i. e., coefficients S, are the components of the eigenvectors of some Hermitian matrices, and can be made as real numbers for all pure rotation point groups. The general formula for coefficient S was deduced, and applied to constructing the basis functions of single-valued irreducible representations of icosahedral group from the spherical harmonics with angular momentum j≤7.

关键词： irreducible representation Basis function I group Angular momentum

Construct Weak Hopf Algebras by Using Borcherds Matrix

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Acta Mathematica Sinica,English Series 2009年第8期25卷 1337-1352页

作者： Zhi Xiang WU Department of Mathematics Zhejiang University Hangzhou 310027 P. R. China

We define a new kind quantized enveloping algebra of a generalized Kac-Moody algebra by adding a new generator J satisfying jm = j for some integer m. We denote this algebra by wUqT（A）. This algebra is a weak Hopf algebra if and only if m = 2,3. In general, it is a bialgebra, and contains a Hopf subalgebra. This Hopf subalgebra is isomorphic to the usual quantum envelope algebra Uq （A） of a generalized Kac-Moody algebra A.

关键词： generalized Kac-Moody algebras irreducible representation weak Hopf algebra

Uniqueness of twisted linear periods and twisted Shalika periods

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Science China Mathematics 2020年第1期63卷 1-22页

作者： Fulin Chen Binyong Sun School of Mathematical Sciences Xiamen UniversityXiamen 361005China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100190China

Let k be a local field of characteristic ***πbe an irreducible admissible smooth representation of GL2 n(k).We prove that for all but countably many charactersχ’s of GLn(k)×GLn(k),the space ofχ-equivariant(continuous in the archimedean case)linear functionals onπis at most one *** this,we prove the uniqueness of twisted Shalika models.

关键词： linear period Shalika model irreducible representation uniqueness generalized function

On representations of real Jacobi groups

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Science China Mathematics 2012年第3期55卷 541-555页

作者： SUN BinYong Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

We consider a category of continuous Hilbert space representations and a category of smooth Fr'echet representations,of a real Jacobi group *** Mackey's theory,they are respectively equivalent to certain categories of representations of a real reductive group *** these categories,we show that the two functors that take smooth vectors for G and for L are consistent with each *** using Casselman-Wallach's theory of smooth representations of real reductive groups,we define matrix coefficients for distributional vectors of certain representations of *** also formulate Gelfand-Kazhdan criteria for real Jacobi groups which could be used to prove multiplicity one theorems for Fourier-Jacobi models.

关键词： Jacobi group Heisenberg group irreducible representation matrix coefficient Gelfand-Kazhdancriterion

Square Integrable representation of Groupoids

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Acta Mathematica Sinica,English Series 2007年第2期23卷 327-340页

作者： H.AMIRI M.LASHKARIZADEH BAMI Department of Mathematics University of Isfahan

A notion of an irreducible representation, as well as of a square integrable representation on an arbitrary locally compact groupoid, is introduced. A generalization of a version of Schur＇s lemma on a locally compact groupoid is given. This is used in order to extend some well-known results from locally compact groups to the case of locally compact groupoids. Indeed, we have proved that if L is a continuous irreducible representation of a compact groupoid G defined by a continuous Hilbert bundle H = （Hu）u∈G^0, then each Hu is finite dimensional. It is also shown that if L is an irreducible representation of a principal locally compact groupoid defined by a Hilbert bundle （G^0, （Hu）,μ）, then dimHu = 1 （u ∈ G^0）. Furthermore it is proved that every square integrable representation of a locally compact groupoid is unitary equivalent to a subrepresentation of the left regular representation. Furthermore, for r-discrete groupoids, it is shown that every irreducible subrepresentation of the left regular representation is square integrable.

关键词： topological groupoid irreducible representation square integrable representation

The C-G coefficients for the space group D_6~1h

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Journal of Harbin Institute of Technology(New Series) 2006年第1期13卷 23-26页

作者：王爱芬 School of Science Hangzhou Dianzi University Hangzhou 310012 China

In this paper, the eigenfunction method established by Chen Jin-quan is used to compute the C-G coefficients in regard to the coupling between symmetry points and lines in the first Brillouin zone of the structure D6h^1, space group. Therewith, the wave vector selection rule and the C-G series, are also given as the middle result of computing the C-G coefficients.

关键词： space group irreducible representation eigenfunction method class operator C-G coefficient