Schur Q-functions were originally introduced by Schur in relation to projective representations of the symmetric group and they can be defined combinatorially in terms of shifted tableaux. In this paper we describe planar decompositions of shifted tableaux into strips and use the shapes of these strips to generate pfaffi.ans and determinants that are equal to Schur Q-functions. As special cases...

We introduce a new basis for the algebra of quasisymmetric functions that naturally partitions Schur functions, called quasisymmetric Schur functions. We describe their expansion in terms of fundamental quasisymmetric functions and determine when a quasisymmetric Schur function is equal to a fundamental quasisymmetric function. We conclude by describing a Pieri rule for quasisymmetric Schur fun...

We consider a stationary Stokes problem with a piecewise constant viscosity coefficient. For the variational formulation of this problem in H0 × L2 we prove a well-posedness result in which the constants are uniform with respect to the jump in the viscosity coefficient. For a standard discretization with a pair of LBB stable finite element spaces we prove an infsup stability result uniform with...

We present a survey of recent developments of the Beilinson–Lusztig–MacPherson approach in the study of quantum gl n , infinitesimal quantum gl n , quantum gl ∞ and their associated q-Schur algebras, little q-Schur algebras and infinite q-Schur algebras. We also use the relationship between quantum gl ∞ and infinite q-Schur algebras to discuss their representations.

The paper presents a general combinatorial approach to the Schur functions and their modiications, respective generalized Cauchy identities, and bijective Knuth-type correspondences between matrices and pairs of tableaux. All of these appear whenever one has a pair of graphs with the same vertices such that the linear operators associated with these graphs satisfy a certain type of commutation ...

We present special Newton-multigrid techniques for stationary incompressible nonlinear flow models discretised by the high order LBB-stable Q2P1 element pair. We treat the resulting nonlinear and the corresponding linear discrete systems by a fully coupled monolithic approach to maintain high accuracy and robustness, particularly with respect to different rheological behaviour but also regardin...

Using operators on compositions we develop further both the theory of quasisymmetric Schur functions and of noncommutative Schur functions. By establishing relations between these operators, we show that the posets of compositions arising from the right and left Pieri rules for noncommutative Schur functions can each be endowed with both the structure of dual graded graphs and dual filtered gra...

Many results involving Schur functions have analogues involving k-Schur functions. Standard strong marked tableaux play a role for k-Schur functions similar to the role standard Young tableaux play for Schur functions. We discuss results and conjectures toward an analogue of the hook-length formula.