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Finally the cubic surfaces of each component ofQ are studied in details by determining their stabilizers, their rational representations and whether they can be expressed as the determinant of a 3×3 matrix of linear forms.
      
In this paper we present an explicit formula for the twistors in the form of an infinite product of the universalR matrix ofUq(g).
      
Semi-invariants of quivers can be constructed by taking admissible partial polarizations of the determinant of matrices containing sums of matrix components of the representation and the identity matrix as blocks.
      
These are analogous to "fusion rules" in tensor product decomposition and their derivation obtains from an analysis of theR-matrix.
      
The form of these generic polynomials is that of a Bethe eigenfunction and they imitate, on a more elementary level, the R-matrix construction of quantum immanants.
      
Can one factor the classical adjoint of a generic matrix
      
Let k be an integral domain, n a positive integer, X a generic n × n matrix over k (i.e., the matrix (xij over a polynomial ring k[xij] in n2 indeterminates xij), and adj(X) its classical adjoint.
      
The operation adj on matrices arises from the (n - 1)st exterior power functor on modules; the analogous factorization question for matrix constructions arising from other functors is raised, as are several other questions.
      
Haas asked whether for every expanding integer matrix
      
The frame operator of this sequence is expressed as a matrix-valued function multiplying a vector-valued function.
      
An important property of this matrix is that the maximum and minimum eigenvalues are equal (in some sense) to the upper and lower frame bounds.
      
Using the matrix approach we prove that the sequence of sampling functions is always complete in the cases of critical sampling and oversampling.
      
Finally, the matrix approach can be similarly applied to other problems of signal representation.
      
The constants obtained are independent of the dimension n and depend only on k,p, and the number of different eigenvalues of the matrix B.
      
Let A be an expanding n × n integer matrix with |det (A)| = m.
      
Let A be an expanding n×n integer matrix with |det(A)|=m.
      
A corollary is the existence of wavelet sets, and hence of single-function wavelets, for arbitrary expansive matrix dilations on L2(?n).
      
Moreover, for any expansive matrix dilation, it is proven that there are sufficiently many wavelet sets to generate the Borel structure of?n.
      
Orthogonality conditions for ?1, …, ?q naturally impose constraints on the scaling coefficients, which are then called the wavelet matrix.
      
Furthermore, we generalize the sufficient and necessary conditions of orthogonality given by Lawton and Cohen to the case of several dimensions and arbitrary dilation matrix A.
      
 

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