Let X λ be the closure of the I-orbit X λ in the affine Grassmanian Gr of a simple algebraic group G of adjoint type, where I is the Iwahori subgroup and λ is a coweight of G. We find a simple algorithm which describes the set Ψ(λ) of all I-orbits in X λ in terms of coweights. We introduce R-operators (associated to positive roots) on the coweight lattice of G, which exactly describe the closure relation of I-orbits. We also establish a duality between the set Ψ(λ) and the weight system of the level one affine Demazure module Dλ of L g indexed by λ, where L g is the affine Kac-Moody algebra dual to the affine Kac-Moody Lie algebra g associated to the Lie algebra g of G.
In this paper, we consider T-colorings of directed graphs. In particular, we consider as a T-set the set T r = {0, 1, 2,. .. , r −1, r +1,. . .}. Exact values and bounds of the T r-span of directed graphs whose underlying graph is a wheel graph are presented.
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