We compute all the relations in cohomology satisfied by the elements of degree two of H∗(Un(Fp), Z) where p ≥ n and Un(Fp) is the group of of upper triangular matrices of GLn(Fp) with 1 on the main diagonal. e-mail: [email protected]

Department of Computer Science, K.U.Leuven Celestijnenlaan 200A B-3001 Heverlee, Belgium In this talk we investigate some matrix structures on Cn×n that have a good behaviour under matrix inversion. The first kind of structure is strongly related to low displacement rank structure. The second kind of structure deals with certain low rank submatrices. In this case, it can be shown that also the ...

where τ0 = 1. The τ -functions τn are given by the pfaffians of certain skew-symmetric matrix. We identify one-soliton solution as an element of the Weyl group of D-type, and discuss a general structure of the interaction patterns among the solitons. Soliton solutions are characterized by 4N × 4N skew-symmetric constant matrix which we call the B-matrices. We then find that one can have M -soli...

We consider positive entropy G-systems for certain countable, discrete, infinite left-orderable amenable groups G. By undertaking local analysis, the existence of asymptotic pairs and chaotic sets will be studied in connecting with the stable sets. Examples are given for the case of integer lattice groups, the Heizenberg group, and the groups of integral unipotent upper triangular matrices.

We characterize T-measures on weakly generated tribes, where T is a strict triangular norm and we give a Liapunoff Theorem for these measures. This generalizes previous results obtained for monotonic T-measures or for Frank triangular norms.

The fine spectra of lower triangular double-band matrices were examined by several authors. Here we determine the fine spectra of upper triangular double-band matrices over the sequence spaces () p and () bv p. Upper triangular double-band matrices are infinite matrices which include the left-shift, averaging and difference operators.

Block lower triangular matrices and block upper triangular matrices are popular preconditioners for 2×2 block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned matrices are related.

We study the de Rham 1-cohomology H 1 DR (M, G) of a smooth manifold M with values in a Lie group G. By definition, this is the quotient of the set of flat connections in the trivial principal bundle M × G by the so-called gauge equivalence. We consider the case when M is a compact Kähler manifold and G is a solvable complex linear algebraic group of a special class which contains the Borel sub...

We discuss an open problem on the discreteness of subgroups of (SL2(R)) (n ≥ 2) generated by n linearly independent upper triangular matrices and n linearly independent lower triangular matrices. According to a conjecture by Margulis, only Hilbert modular groups can arise this way. The purpose of this note is to explain how this open problem is related to another conjecture on the orbit behavio...

Let 1 < p < ∞ and A = (an,k)n,k 1 be a non-negative matrix. Denote by ‖A‖w,p,F , the infimum of those U satisfying the following inequality: ‖Ax‖w,p,F U ‖x‖w,p,I , where x 0 and x ∈ lp(w,I) and also w = (wn)n=1 is a decreasing, non-negative sequence of real numbers. The purpose of this paper is to give a lower bound for ‖A‖w,p,F , where A is a lower triangular matrix. In particular, we apply ou...