This paper builds upon the work of Cline [C] and Donkin [D1] to describe explicit equivalences between some categories associated to the category of rational modules for a reductive group G and categories associated to the category of rational modules for a Levi subgroup H . As an application, we establish an Ext-transfer result from rational G-modules to rational H-modules. In case G = GLn, th...

Mason and Remmel introduced a basis for quasisymmetric functions known as the row-strict quasisymmetric Schur functions. This basis is generated combinatorially by fillings of composition diagrams that are analogous to the row-strict tableaux that generate Schur functions. We introduce a modification known as Young row-strict quasisymmetric Schur functions, which are generated by row-strict You...

This paper considers an algebraic preconditioning algorithm for hyperbolicelliptic fluid flow problems. The algorithm is based on a parallel non-overlapping Schur complement domain-decomposition technique for triangulated domains. In the Schur complement technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. This suggests a reordering of tr...

Let S(Λ) be the cyclotomic q-Schur algebra associated to the ArikiKoike algebra H . We construct a certain subalgebra S(Λ) of S(Λ), and show that it is a standardly based algebra in the sense of Du and Rui. S(Λ) has a natural quotient S(Λ), which turns out to be a cellular algebra. In the case where the modified Ariki-Koike algebra H ♭ is defined, S(Λ) coincides with the cyclotomic q-Schur alge...

The goal of this paper is the construction of a data-sparse approximation to the Schur complement on the interface corresponding to FEM and BEM approximations of an elliptic equation by domain decomposition. Using the hierarchical (H-matrix) formats we elaborate the approximate Schur complement inverse in an explicit form. The required cost O(NΓ log q NΓ ) is almost linear in NΓ – the number of...

We present a class of domain decomposition (DD) preconditioners for the solution of elliptic linear-quadratic optimal control problems. Our DD preconditioners are extensions of Neumann–Neumann DD preconditioners, which have been successfully applied to the solution of single PDEs. The DD preconditioners are based on a decomposition of the optimality conditions for the elliptic linear-quadratic ...

Let n ≥ 4 be an even integer. Let K be a field with charK 6= 2 and q an invertible element in K such that Qn−1 i=1 (1+q ) 6= 0. In this paper, we study the decomposition numbers over K of the Iwahori–Hecke algebra Hq(Dn) of type Dn. We obtain some equalities which relate its decomposition numbers with certain Schur elements and the decomposition numbers of various Iwahori–Hecke algebras of type...

Abstract. A fast method for solving a linear system of the form (A(p) ⊗ · · · ⊗ A(1) − λI)x = b is given where each A(i) is an ni-by-ni matrix. The first step is to convert the problem to triangular form (T (p) ⊗ · · · ⊗ T (1) − λI)y = c by computing the (complex) Schur decompositions of the A(i). This is followed by a recursive back-substitution process that fully exploits the Kronecker struct...

In a recent article [8], Gowda and Sznajder studied the concept of Schur complement in Euclidean Jordan algebras and described Schur determinantal and Haynsworth inertia formulas. In this article, we establish some more results on the Schur complement. Specifically, we prove, in the setting of Euclidean Jordan algebras, an analogue of the Crabtree-Haynsworth quotient formula and show that any S...