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1. Bertaccini, Daniele

et al.

Donatelli, Marco

Durastante, Fabio

Serra-Capizzano, Stefano

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

We classify simple weight modules with finite-dimensional weight spaces over the (centrally extended complex) Schrodinger algebra in (1 + 1)-dimensional space-time. Our arguments use the description of lowest weight modules by Dobrev, Doebner and Mrugalla; Mathieu's twisting functors and results of Wu and Zhu on dimensions of weight spaces in dense modules.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.

Lu, Rencai

Mazorchuk, Volodymyr

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.

Zhao, Kaiming

Category O for the Schrodinger algebra2014In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 460, p. 17-50Article in journal (Refereed)

Abstract [en]

We study category O for the (centrally extended) Schrodinger algebra. We determine the quivers for all blocks and relations for blocks of nonzero central charge. We also describe the quiver and relations for the finite dimensional part of O. We use this to determine the center of the universal enveloping algebra and annihilators of Verma modules. Finally, we classify primitive ideals of the universal enveloping algebra which intersect the center of the centrally extended Schrodinger algebra trivially.

A general introduction is given to the logarithmic q-analogue formulation of mathematical expressions with a special focus on its use for matrix calculations. The fundamental definitions relevant to q-analogues of mathematical objects are given and form the basis for matrix formulations in the paper. The umbral approach is used to find q-analogues of significant matrices. Finally, as an explicit example, a new formula for q-Cauchy-Vandermonde determinant containing matrix elements equal to q-numbers introduced by Ward is proved by using a new type of q-Stirling numbers together with Lagrange interpolation in Z(q).

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

A converse to the Bauer-Fike theorem1974In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 9, p. 267-274Article in journal (Refereed)

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

A new type of complex Hadamard matrices of order 9 are constructed. The studied matrices are symmetric, block circulant with circulant blocks (BCCB) and form an until now unknown non-reducible and non-affine two-parameter orbit. Several suborbits are identified, including a one parameter intersection with the Fourier orbit F-9((4)). The defect of this new type of Hadamard matrices is observed to vary, from a generic value 2 to the anomalous values 4 and 10 for some sub-orbits, and to 12 and 16 for some single matrices. The latter matrices are shown to be related to complete sets of MUBs in dimension 9.

Complex Hadamard matrices H of order 6 are characterized in a novel manner, according to the presence/absence of order 2 Hadamard submatrices. It is shown that if there exists one such submatrix. H is equivalent to a Hadamard matrix where all the nine submatrices are Hadamard. The ensuing subset of H-2-reducible complex Hadamard matrices is more general than might be thought, and, significantly, includes all the up till now described (one- and two-parameter) families of order 6. A known, isolated matrix, and most numerically generated matrices, fall outside the subset.

A three-parameter family of complex Hadamard matrices of order 6 is presented. It significantly extends the set of closed form complex Hadamard matrices of this order, and in particular contains all previously described one- and two-parameter families as subfamilies.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.

We prove the Cauchy-Binet determinantal formula using multilinear algebra by first generalizing it to an identity not involving determinants. By extending the formula to abstract Hilbert spaces we obtain, as a corollary, a generalization of the classical Parseval identity.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.