We show that the problem of deciding membership in the moment polytope associated with a finite-dimensional unitary representation of a compact, connected Lie group is in NP ∩ coNP. This is the first non-trivial result on the computational complexity of this problem, which naively amounts to a quadratically-constrained program. Our result applies in particular to the Kronecker polytopes, and th...

Kronecker coefficients encode the tensor products of complex irreducible representations of symmetric groups. Their stability properties have been considered recently by several authors (Vallejo, Pak and Panova, Stembridge). In [3] we described a geometric method, based on Schur-Weyl duality, that allows to produce huge series of instances of this phenomenon. In this note we show how to go beyo...

We study, in type A, the algebraic cycles (MV-cycles) discovered by I. Mirkovi´c and K. Vilonen [MV]. In particular, we partition the loop Grassmannian into smooth pieces such that the MV-cycles are their closures. We explicitly describe the points in each piece using the lattice model of the loop Grassmannian in type A. The partition is invariant under the action of the coweights and, up to th...

Let u and v be permutations on n letters, with u ≤ v in Bruhat order. A Bruhat interval polytope Qu,v is the convex hull of all permutation vectors z = (z(1), z(2), . . . , z(n)) with u ≤ z ≤ v. Note that when u = e and v = w0 are the shortest and longest elements of the symmetric group, Qe,w0 is the classical permutohedron. Bruhat interval polytopes were studied recently in the 2013 paper “The...

We consider the semigroup $S$ of highest weights appearing in tensor powers $V^{otimes k}$ of a finite dimensional representation $V$ of a connected reductive group. We describe the cone generated by $S$ as the cone over the weight polytope of $V$ intersected with the positive Weyl chamber. From this we get a description for the asymptotic of the number of highest weights appearing in $V^{otime...

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Objective(s): The results of studies on vaccine development for foot-and-mouth disease (FMD) virus show that the use of inactivated vaccines for FMD virus is not completely effective. Novel vaccinations based on immuno-dominant epitopes have been shown to induce immune responses. Furthermore, for safety of immunization, access to efficient adjuvants against FMD virus seems to be critical.Materi...