Results 1 to 10 of about 32,198 (104)
Grassmann and Flag Varieties in Linear Algebra, Optimization, and Statistics: An Algebraic Perspective [PDF]
Grassmann and flag varieties lead many lives in pure and applied mathematics. Here we focus on the algebraic complexity of solving various problems in linear algebra and statistics as optimization problems over these varieties. The measure of the algebraic complexity is the amount of complex critical points of the corresponding optimization problem ...
Friedman, Hannah, Hoşten, Serkan
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Inverse K-Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type
Forum of Mathematics, Sigma, 2021 We prove an explicit inverse Chevalley formula in the equivariant K-theory of semi-infinite flag manifolds of simply laced type. By an ‘inverse Chevalley formula’ we mean a formula for the product of an equivariant scalar with a Schubert class, expressed
Takafumi Kouno +3 more
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Accessible Proof of Standard Monomial Basis for Coordinatization of Schubert Sets of Flags [PDF]
, 2015 The main results of this paper are accessible with only basic linear algebra. Given an increasing sequence of dimensions, a flag in a vector space is an increasing sequence of subspaces with those dimensions. The set of all such flags (the flag manifold)
Lax, David C.
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Alcove path and Nichols-Woronowicz model of the equivariant $K$-theory of generalized flag varieties [PDF]
, 2006 Fomin and Kirillov initiated a line of research into the realization of the cohomology and $K$-theory of generalized flag varieties $G/B$ as commutative subalgebras of certain noncommutative algebras.
Lenart, Cristian, Maeno, Toshiaki
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Analysis of Fuzzy Vector Spaces as an Algebraic Framework for Flag Codes
MathematicsFlag codes are a recent network coding strategy based on linear algebra. Fuzzy vector subspaces extend the notions of classical linear algebra. They can be seen as abstractions of flags to the point that several fuzzy vector subspaces can be identified ...
Carlos Bejines +2 more
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Perverse sheaves, Koszul IC-modules, and the quiver for the category O
, 2006 For a stratified topological space we introduce the category of IC-modules, which are linear algebra devices with the relations described by the equation d^2=0.
Vybornov, Maxim
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Solvability of the Hamiltonians related to exceptional root spaces: rational case
, 2004 Solvability of the rational quantum integrable systems related to exceptional root spaces $G_2, F_4$ is re-examined and for $E_{6,7,8}$ is established in the framework of a unified approach.
Alexander V. Turbiner +13 more
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Categorification of skew-symmetrizable cluster algebras
, 2009 We propose a new framework for categorifying skew-symmetrizable cluster algebras. Starting from an exact stably 2-Calabi-Yau category C endowed with the action of a finite group G, we construct a G-equivariant mutation on the set of maximal rigid G ...
A Berenstein +36 more
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, 2010 We present an application of the program of groupoidification leading up to a sketch of a categorification of the Hecke algebroid --- the category of permutation representations of a finite group. As an immediate consequence, we obtain a categorification
Hoffnung, Alexander E.
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Grassmannians and Koszul duality
, 2014 Let $X$ be a partial flag variety, stratified by orbits of the Borel. We give a criterion for the category of modular perverse sheaves to be equivalent to modules over a Koszul ring. This implies that modular category $\mathcal O$ is governed by a Koszul-
Weidner, Jan
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