We characterize the initial terms under a diagonal term order of the supersymmetric Schur/Weyl module S(V V ) associated to a row-convex shape D. We show the biwords corresponding to the initial terms of S are closed under dual-Knuth equivalence and that the recording tableaux for these words are decomposable in the sense of [10]. We consider the natural action of bases of S in which the elemen...

We study the large scale geometry of the upper triangular subgroup of PSL2(Z[ 1 n ]), which arises naturally in a geometric context. We prove a quasi-isometry classification theorem and show that these groups are quasi-isometrically rigid with infinite dimensional quasi-isometry group. We generalize our results to a larger class of groups which are metabelian and are higher dimensional analogue...

Article history: Received 12 September 2015 Accepted 21 December 2015 Available online xxxx Submitted by R. Brualdi MSC: primary 05E15 secondary 15A21

A triangular matrix algebra over a field k is defined by a triplet (R, S, M) where R and S are k-algebras and RMS is an SR-bimodule. We show that if R, S and M are finite dimensional and the global dimensions of R and S are finite, then the triangular matrix algebra corresponding to (R, S, M) is derived equivalent to the one corresponding to (S, R, DM), where DM = Homk(M, k) is the dual of M , ...

We describe an extension to ScaLAPACK for computing with symmetric (and hermitian) matrices stored in a packed form. This is similar to the compact storage for symmetric (and hermitian) matrices available in LAPACK [2]. This enables more efficient use of memory by storing only the lower or upper triangular part of a symmetric matrix. The capabilities include Choleksy factorization (PxSPTRF) and...

Some approaches to 2d gravity developed for the last years are reviewed. They are physical (Liouville) gravity, topological theories and matrix models. A special attention is paid to matrix models and their interrelations with different approaches. Almost all technical details are omitted, but examples are presented.

We prove a lower bound of 52n2 3n for the rank of n n–matrix multiplication over an arbitrary field. Similar bounds hold for the rank of the multiplication in noncommutative division algebras and for the multiplication of upper triangular matrices.