- Full text PDF available (18)
The metaplectic representation describes a class of automorphisms of the Heisenberg group H = H (G), defined for a locally compact abelian group G. For G = R d , H is the usual Heisenberg group. For the case when G is the finite cyclic group Z n , only partial constructions are known. Here we present new results for this case and we obtain an explicit… (More)
In this lecture I discuss some aspects of MKM, Mathematical Knowledge Management, with particuar emphasis on information storage and information retrieval. 1. Is there a problem? The issue at hand is that of information storage and information retrieval as regards mathematics. Or, concentrating on the latter, if one has a mathematical question, can one find… (More)
Introduction. The subject of this discussion paper is information storage and, especially, information retrieval from large and very large collections of objects. The focus is on scientific objects such as papers, tables, programs, handbooks, manuals, .... All of these will be referred to here and below as documents. They can be quite heterogeneous in form… (More)
Let A be a bipartite graph between two sets D and T. Then A defines by Hamming distance, metrics on both T and D. The question is studied which pairs of metric spaces can arise this way. If both spaces are trivial the matrix A comes from a Hadamard matrix or is a BIBD. The second question studied is in what ways A can be used to transfer (classification)… (More)
Let A be a reduced incidence relation between n lines and m points. Suppose that (a) Through each two points there pass λ lines (b) Each two lines intersect in µ points. If λ µ = = 1 assume, moreover, that there are four points no three of which are on one line. Then n m = , λ µ = , and there is a number r such that all lines have r points and through each… (More)
Let Z denote the free associative algebra ZhZ1; Z2 ; : : :i over the integers. This algebra carries a Hopf algebra structure for which the comultiplication is Zn 7 ! i+j=nZi Zj. This the noncommutative Leibniz-Hopf algebra. It carries a natural grading for which gr(Zn) = n. The Ditters-Scholtens theorem says that the graded dual, M, of Z, herein called the… (More)
Using methods from the geometric theory of quiver representations, moduli spaces of linear control systems are described as vector bundles over Grassmannians. Inspired by ideas from non-commutative geometry, unions of such moduli spaces are identified as open subsets of infinite Grassmannians.