Dissimilarity Vectors of Trees and Their Tropical Linear Spaces (Extended Abstract) by Benjamin Iriarte Giraldo

“…The set of dissimilarity vectors of weighted trees is contained in the tropical Grassmannian, so we describe here the tropical linear space of a dissimilarity vector and its associated family of matroids. …”
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Tree-level gluon amplitudes on the celestial sphere by Anders Ø. Schreiber, Anastasia Volovich, Michael Zlotnikov

“…The Mellin transforms of MHV amplitudes are given by generalized hypergeometric functions on the Grassmannian Gr(4,n), while generic non-MHV amplitudes are given by more complicated Gelfand A-hypergeometric functions.…”
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Product of Stanley symmetric functions by Nan Li

“…In the case when one permutation is Grassmannian, we have a better understanding of this stability.…”
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Quasi-isomorphisms of cluster algebras and the combinatorics of webs (extended abstract) by Chris Fraser

“…Using our bijection and symmetries of these cluster algebras, we provide evidence for conjectures of Fomin and Pylyavskyy concerning cluster variables in Grassmannians of 3-planes. We also prove their conjecture that there are infinitely many indecomposable nonarborizable webs in the Grassmannian of 3-planes in 9-dimensional space.…”
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Matroid Polytopes and Their Volumes by Federico Ardila, Carolina Benedetti, Jeffrey Doker

“…This gives a combinatorial expression for the degree of an arbitrary torus orbit closure in the Grassmannian $Gr_{k,n}$. We then derive analogous results for the independent set polytope and the associated flag matroid polytope of $M$. …”
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New Characterizations of the Clifford Torus and the Great Sphere by Sun Mi Jung, Young Ho Kim, Jinhua Qian

“…In studying spherical submanifolds as submanifolds of a round sphere, it is more relevant to consider the spherical Gauss map rather than the Gauss map of those defined by the oriented Grassmannian manifold induced from their ambient Euclidean space. …”
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General composite non-Abelian strings and flag manifold sigma models by Edwin Ireson

“…After spontaneous symmetry breaking, there remains some internal color degrees of freedom attached to these objects, which we argue must exist in a flag manifold, a more general kind of projective space than both CP(N) and the Grassmannian manifold. These strings are expected to be Bogomol'nyi-Prasad-Sommerfeld since its constituents are. …”
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Links in the complex of weakly separated collections by Suho Oh, David Speyer

“…Plabic graphs are combinatorial objects used to study the totally nonnegative Grassmannian. Faces of plabic graphs are labeled by k-element sets of positive integers, and a collection of such k-element sets are the face labels of a plabic graph if that collection forms a maximal weakly separated collection. …”
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Double Schubert polynomials for the classical Lie groups by Takeshi Ikeda, Leonardo Mihalcea, Hiroshi Naruse

“…When indexed by maximal Grassmannian elements of the Weyl group, these polynomials are equal to the factorial analogues of Schur $Q$- or $P$-functions defined earlier by Ivanov.…”
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The Loop Momentum Amplituhedron by Livia Ferro, Tomasz Łukowski

“…Motivated by the structure of amplitude singularities, we define an extended positive space, which enhances the Grassmannian space featuring at tree level, and a map which associates to each of its points tree-level kinematic variables and loop momenta. …”
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Moduli spaces of sheaves on surfaces: Hecke correspondences and representation theory by Neguţ, A

“…For example, the moduli space of linear subspaces of 𝔸n is the Grassmannian variety, which is a classical object in representation theory. …”
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Tree-level recursion relation and dual superconformal symmetry of the ABJM theory by Gang, D, Huang, Y, Koh, E, Lee, S, Lipstein, A

“…Furthermore, we use the recursion relation to compute six-point and eight-point component amplitudes and match them with independent computations based on Feynman diagrams or the Grassmannian integral formula. As an application of the recursion relation, we prove that all tree-level amplitudes of the ABJM theory have dual superconformal symmetry. …”

Tau functions and the twistor theory of integrable systems by Mason, L, Singer, M, Woodhouse, N

“…We first define τ-functions as generalized cross-ratios of four points on a finite- or infinite-dimensional Grassmannian. We show how this definition can be used to construct a natural flat connection on a determinant line bundle associated with two equivariant holomorphic vector bundles over a twistor space, provided that the action of the symmetries on the bundles has the same normal form at the fixed points for the two bundles. …”

Tree-level Recursion Relation and Dual Superconformal Symmetry of the ABJM Theory by Gang, D, Huang, Y, Koh, E, Lee, S, Lipstein, A

“…Furthermore, we use the recursion relation to compute six-point and eight-point component amplitudes and match them with independent computations based on Feynman diagrams or the Grassmannian integral formula. As an application of the recursion relation, we prove that all tree-level amplitudes of the ABJM theory have dual superconformal symmetry. …”

Expected values of statistics on permutation tableaux by Sylvie Corteel, Pawel Hitczenko

“…Permutation tableaux are new objects that were introduced by Postnikov in the context of enumeration of the totally positive Grassmannian cells. They are known to be in bijection with permutations and recently, they have been connected to PASEP model used in statistical physics. …”
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Celestial amplitudes in an ambidextrous basis by Carmen Jorge-Diaz, Sabrina Pasterski, Atul Sharma

“…Finally, we focus on the tree level 4-gluon amplitude where we present a streamlined route to the ambidextrous correlator based on Grassmannian formulae and examine its alpha space representation. …”
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Weak Separation, Pure Domains and Cluster Distance by Miriam Farber, Pavel Galashin

“…We apply our result to calculate the cluster distance and to give lower bounds on the mutation distance between cluster variables in the cluster algebra structure on the coordinate ring of the Grassmannian. Using a linear projection that relates weak separation to the octahedron recurrence, we also find the exact mutation distances and cluster distances for a family of cluster variables.…”
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Polypositroids by Thomas Lam, Alexander Postnikov

“…Whereas positroids are the matroids arising from the totally nonnegative Grassmannian, polypositroids are “positive” polymatroids. …”
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Path integral quantization of generalized Stueckelberg electrodynamics: A Faddeev-Jackiw approach by L.G. Caro, G.B. de Gracia, A.A. Nogueira, B.M. Pimentel

“…We build a setup for path integral quantization through the Faddeev-Jackiw approach, extending it to include Grassmannian degrees of freedom, to be later implemented in a model of generalized electrodynamics that involves fourth-order derivatives in the components of a massive vector field being endowed with gauge freedom, due to an additional scalar field. …”
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Ambidextrous light transforms for celestial amplitudes by Atul Sharma

“…We also study such amplitudes at higher multiplicity by constructing the Grassmannian representation of tree-level gluon celestial amplitudes as well as their light transforms. …”
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