Sects and Lattice Paths over the Lagrangian Grassmannian
نویسندگان
چکیده
منابع مشابه
Quantum Cohomology of the Lagrangian Grassmannian
Let V be a symplectic vector space and LG be the Lagrangian Grassmannian which parametrizes maximal isotropic subspaces in V . We give a presentation for the (small) quantum cohomology ring QH∗(LG) and show that its multiplicative structure is determined by the ring of Q̃-polynomials. We formulate a ‘quantum Schubert calculus’ which includes quantum Pieri and Giambelli formulas, as well as algor...
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The Drinfel’d Lagrangian Grassmannian compactifies the space of algebraic maps of fixed degree from the projective line into the Lagrangian Grassmannian. It has a natural projective embedding arising from the canonical embedding of the Lagrangian Grassmannian. We show that the defining ideal of any Schubert subvariety of the Drinfel’d Lagrangian Grassmannian is generated by polynomials which gi...
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Let LGn denote the Lagrangian Grassmannian parametrizing maximal isotropic (Lagrangian) subspaces of a fixed symplectic vector space of dimension 2n. For each strict partition λ = (λ1, . . . , λk) with λ1 ≤ n there is a Schubert variety X(λ). Let T denote a maximal torus of the symplectic group acting on LGn. Consider the T -equivariant cohomology of LGn and the T -equivariant fundamental class...
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Using Plücker coordinates we construct a matrix whose columns parametrize all projective isotropic lines in a symplectic space E of dimension 4 over a finite field Fq. As an application of this construction we explicitly obtain the smallest subfamily of algebro-geometric codes defined by the corresponding Lagrangian-Grassmannian variety. Furthermore, we show that this subfamily is a class of th...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2020
ISSN: 1077-8926
DOI: 10.37236/8664