We study certain monoidal subcategories (introduced by David Hernandez and Bernard Leclerc) of finite-dimensional representations of a quantum affine algebra of type A. We classify the set of prime representations in these subcategories and give necessary and sufficient conditions for a tensor product of two prime representations to be irreducible. In the case of a reducible tensor product we describe the prime decomposition of the simple factors. As a consequence we prove that these subcategories are monoidal categorifications of a cluster algebra of type A with coefficients.

It is undeniable that aerial/satellite images can provide useful information for a large variety of tasks. But, since these images are always looking from above, some applications can benefit from complementary information provided by other perspective views of the scene, such as ground-level images. Despite a large number of public repositories for both georeferenced photographs and aerial images, there is a lack of benchmark datasets that allow the development of approaches that exploit the benefits and complementarity of aerial/ground imagery. In this paper, we present two new publicly available datasets named AiRound and CV-BrCT. The first one contains triplets of images from the same geographic coordinate with different perspectives of view extracted from various places around the world. Each triplet is composed of an aerial RGB image, a ground-level perspective image, and a Sentinel-2 sample. The second dataset contains pairs of aerial and street-level images extracted from southeast Brazil. We design an extensive set of experiments concerning multi-view scene classification, using early and late fusion. Such experiments were conducted to show that image classification can be enhanced using multi-view data.

We study the classical limit of a family of irreducible representations of the quantum affine algebra associated to sln+1. After a suitable twist, the limit is a module for sln+1[t], i.e., for the maximal standard parabolic subalgebra of the affine Lie algebra. Our first result is about the family of prime representations introduced in [28], [30], in the context of a monoidal categorification of cluster algebras. We show that these representations specialize (after twisting), to sln+1[t]-stable, prime Demazure modules in level two integrable highest weight representations of the classical affine Lie algebra. It was proved in [18] that a stable Demazure module is isomorphic to the fusion product of stable, prime Demazure modules. Our next result proves that such a fusion product is the limit of the tensor product of the corresponding irreducible prime representations of quantum affine sln+1.

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