We relate the canonical basis of the Fock space representation of the quantum affine algebra Uq(ĝln), as defined by Leclerc and Thibon [LT], to the canonical basis of its restriction to Uq(sln), regarded as a based module in the sense of Lusztig. More generally we consider the restriction to any Levi subalgebra. We deduce results on decomposition numbers and branching coefficients of Schur alge...

Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/repns/notes 2014-15/03 generalities finite.pdf] 1. Subrepresentations, complete reducibility, unitarization 2. Dual/contragredient representations 3. Regular and biregular representations L(G) 4. Schur’s lemma 5. Central characters of irreducibles 6. Tensor products of repres...

We prove that every Ariki–Koike algebra is Morita equivalent to a direct sum of tensor products of smaller Ariki–Koike algebras which have q–connected parameter sets. A similar result is proved for the cyclotomic q–Schur algebras. Combining our results with work of Ariki and Uglov, the decomposition numbers for the Ariki–Koike algebras defined over fields of characteristic zero are now known in...

We consider the problem of approximating the generalized Schur decomposition of a matrix pencil A XB by a family of differentiable orthogonal transformations. It is shown that when B is nonsingular this approach is feasible and can be fully expressed as an autonomous differential system. When B is singular, we show that the location of zero diagonal entries of B affects the feasibility of such ...

Dedicated to Olof B. Widlund on the occasion of his 60th birthday. Summary. It is shown that for elliptic boundary value problems of order 2m the condition number of the Schur complement matrix that appears in nonoverlapping domain decomposition methods is of order d ?1 h ?2m+1 , where the parameter d measures the diameters of the subdomains and h is the mesh size of the triangulation. The resu...

In this article, a reduced vector potential formulation for transient magneto-quasistatic field problems is presented. The finite element method spatial discretization yields system of differential algebraic equations (DAE). Applying generalized Schur complement the DAE decomposes into ordinary (ODE) and an equation. order to avoid computationally expensive linearization schemes solve nonlinear...

The usual way to compute a low-rank approximant of a matrix H is to take its singular value decomposition (SVD) and truncate it by setting the small singular values equal to 0. However, the SVD is computationally expensive. This paper describes a much simpler generalized Schur-type algorithm to compute similar low-rank approximants. For a given matrix H which has d singular values larger than ε...

This paper describes a multilevel preconditioning technique for solving linear systems with general sparse symmetric coefficient matrices. This “multilevel Schur low rank” (MSLR) preconditioner first builds a tree structure T based on a hierarchical decomposition of the matrix and then computes an approximate inverse of the original matrix level by level. Unlike classical direct solvers, the co...

The usual way to compute a low-rank approximant of a matrix H is to take its singular value decomposition (SVD) and truncate it by setting the small singular values equal to 0. However, the SVD is computationally expensive. This paper describes a much simpler generalized Schur-type algorithm to compute similar low-rank approximants. For a given matrix H which has d singular values larger than ε...

This report presents a new analytic method for checking the Schur stability of interval polynomial matrix (polynomials whose coefficients are interval matrices). In the suggested method, the interval Markov matrices of the interval polynomial matrix are used to assess its stability. The validity of the suggested method is illustrated through numerical examples. The proposed technique is algebra...