The 6 Vertex Model and Schubert Polynomials
نویسندگان
چکیده
منابع مشابه
The 6 Vertex Model and Schubert Polynomials
We enumerate staircases with fixed left and right columns. These objects correspond to ice-configurations, or alternating sign matrices, with fixed top and bottom parts. The resulting partition functions are equal, up to a normalization factor, to some Schubert polynomials.
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We construct a family of functors assigning an R-module to a flag of R-modules, where R is a commutative ring. As particular instances, we get flagged Schur functors and Schubert functors, the latter family being indexed by permutations. We identify Schubert functors for vexillary permutations with some flagged Schur functors, thus establishing a functorial analogue of a theorem from [6] and [1...
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The Schubert polynomials lift the Schur basis of symmetric polynomials into a basis for Z[x1, x2, . . .]. We suggest the prism tableau model for these polynomials. A novel aspect of this alternative to earlier results is that it directly invokes semistandard tableaux; it does so as part of a colored tableau amalgam. In the Grassmannian case, a prism tableau with colors ignored is a semistandard...
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We obtain a tableau definition of the skew Schubert polynomials named by Lascoux, which are defined as flagged double skew Schur functions. These polynomials are in fact Schubert polynomials in two sets of variables indexed by 321-avoiding permutations. From the divided difference definition of the skew Schubert polynomials, we construct a lattice path interpretation based on the Chen-Li-Louck ...
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The aim of this paper is to introduce some polynomials that specialize to all previously known Schubert polynomials: the classical Schubert polynomials of Lascoux and Schützenberger [L-S], [M], the quantum Schubert polynomials of Fomin, Gelfand, and Postnikov [F-G-P], and quantum Schubert polynomials for partial flag varieties of Ciocan-Fontanine [CF2]. There are also double versions of these u...
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ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2007
ISSN: 1815-0659
DOI: 10.3842/sigma.2007.029