A series of irreducible representations of braid group Bn are given.By means of a generalized Conway relation (gi-q)(gi+p) = 0,a complete set of operators H(i) are constructed.With the eigenvectors of H(i) as represen...A series of irreducible representations of braid group Bn are given.By means of a generalized Conway relation (gi-q)(gi+p) = 0,a complete set of operators H(i) are constructed.With the eigenvectors of H(i) as representation bases,the biparametric irreducible representations of Bn are obtained by the help of Yang diagrams.展开更多
We consider a category of continuous Hilbert space representations and a category of smooth Fr'echet representations,of a real Jacobi group G.By Mackey's theory,they are respectively equivalent to certain cate...We consider a category of continuous Hilbert space representations and a category of smooth Fr'echet representations,of a real Jacobi group G.By Mackey's theory,they are respectively equivalent to certain categories of representations of a real reductive group L.Within these categories,we show that the two functors that take smooth vectors for G and for L are consistent with each other.By using Casselman-Wallach's theory of smooth representations of real reductive groups,we define matrix coefficients for distributional vectors of certain representations of G.We also formulate Gelfand-Kazhdan criteria for real Jacobi groups which could be used to prove multiplicity one theorems for Fourier-Jacobi models.展开更多
Let G be a non-abelian group and let l2(G) be a finite dimensional Hilbert space of all complex valued functions for which the elements of G form the (standard) orthonormal basis. In our paper we prove results concern...Let G be a non-abelian group and let l2(G) be a finite dimensional Hilbert space of all complex valued functions for which the elements of G form the (standard) orthonormal basis. In our paper we prove results concerning G-decorrelated decompositions of functions in l2(G). These G-decorrelated decompositions are obtained using the G-convolution either by the irreducible characters of the group G or by an orthogonal projection onto the matrix entries of the irreducible representations of the group G. Applications of these G-decorrelated decompositions are given to crossover designs in clinical trials, in particular the William’s 6×3?design with 3 treatments. In our example, the underlying group is the symmetric group S3.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘A series of irreducible representations of braid group Bn are given.By means of a generalized Conway relation (gi-q)(gi+p) = 0,a complete set of operators H(i) are constructed.With the eigenvectors of H(i) as representation bases,the biparametric irreducible representations of Bn are obtained by the help of Yang diagrams.
基金supported by National Natural Science Foundation of China(Grant Nos. 10801126 and 10931006)
文摘We consider a category of continuous Hilbert space representations and a category of smooth Fr'echet representations,of a real Jacobi group G.By Mackey's theory,they are respectively equivalent to certain categories of representations of a real reductive group L.Within these categories,we show that the two functors that take smooth vectors for G and for L are consistent with each other.By using Casselman-Wallach's theory of smooth representations of real reductive groups,we define matrix coefficients for distributional vectors of certain representations of G.We also formulate Gelfand-Kazhdan criteria for real Jacobi groups which could be used to prove multiplicity one theorems for Fourier-Jacobi models.
文摘Let G be a non-abelian group and let l2(G) be a finite dimensional Hilbert space of all complex valued functions for which the elements of G form the (standard) orthonormal basis. In our paper we prove results concerning G-decorrelated decompositions of functions in l2(G). These G-decorrelated decompositions are obtained using the G-convolution either by the irreducible characters of the group G or by an orthogonal projection onto the matrix entries of the irreducible representations of the group G. Applications of these G-decorrelated decompositions are given to crossover designs in clinical trials, in particular the William’s 6×3?design with 3 treatments. In our example, the underlying group is the symmetric group S3.
