Trajectory preserving and lifting maps have been implicitly used in many recursive or hierarchical control design techniques. Well known systems theoretic concepts such as differential flatness or more recent ones such as simulation and bisimulation can be also understood through the trajectory lifting maps they define. In this paper we initiate a study of trajectory preserving and lifting maps...

In the large rank limit, for any nonexceptional affine algebra, the graded branching multiplicities known as one-dimensional sums, are conjectured to have a simple relationship with those of type A, which are known as generalized Kostka polynomials. This is called the X = M = K conjecture. It is proved for tensor products of the “symmetric power” Kirillov-Reshetikhin modules for all nonexceptio...

These are (mostly) expository notes for lectures on affine Stanley symmetric functions given at the Fields Institute in 2010. We focus on the algebraic and combinatorial parts of the theory. The notes contain a number of exercises and open problems. Stanley symmetric functions are a family {Fw | w ∈ Sn} of symmetric functions indexed by permutations. They were invented by Stanley [Sta] to enume...

In this article, we prove the following interpolation problem: if composition of a function and regular map between affine varieties is function, then there exists global target variety that coincide with on image provided factorial almost surjective. We also discuss few applications problem.Communicated by Daniel Erman

For a planar curve C with positive affine curvature, we derive an asymptotic formula for the area approximation by quadratic spline curves with n knots lying on C. The order of approximation is 1/n4 and the formula depends on an integral over the affine curvature. 1991 AMS subject classification: 52A10, 53A04, 53A15, 41A15, 41A50

locally extended affine lie algebras were introduced by morita and yoshii in [j. algebra 301(1) (2006), 59-81] as a natural generalization of extended affine lie algebras. after that, various generalizations of these lie algebras have been investigated by others. it is known that a locally extended affine lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...