Schubert polynomials and quiver formulas
نویسندگان
چکیده
منابع مشابه
Schubert Polynomials and Degeneracy Locus Formulas
In previous work [T6], we employed the approach to Schubert polynomials by Fomin, Stanley, and Kirillov to obtain simple, uniform proofs that the double Schubert polynomials of Lascoux and Schützenberger and Ikeda, Mihalcea, and Naruse represent degeneracy loci for the classical groups in the sense of Fulton. Using this as our starting point, and purely combinatorial methods, we obtain a new pr...
متن کاملAlternating Formulas for K-theoretic Quiver Polynomials
The main theorem here is the K-theoretic analogue of the cohomological ‘stable double component formula’ for quiver polynomials in [KMS03]. This K-theoretic version is still in terms of lacing diagrams, but nonminimal diagrams contribute terms of higher degree. The motivating consequence is a conjecture of Buch on the sign-alternation of the coefficients appearing in his expansion of quiver K-p...
متن کاملSchubert functors and Schubert polynomials
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...
متن کاملA Unified Approach to Combinatorial Formulas for Schubert Polynomials
Schubert polynomials were introduced in the context of the geometry of flag varieties. This paper investigates some of the connections not yet understood between several combinatorial structures for the construction of Schubert polynomials; we also present simplifications in some of the existing approaches to this area. We designate certain line diagrams known as rc-graphs as the main structure...
متن کاملGROTHENDIECK POLYNOMIALS AND QUIVER FORMULAS By ANDERS S. BUCH, ANDREW KRESCH, HARRY TAMVAKIS, and ALEXANDER YONG
Fulton’s universal Schubert polynomials give cohomology formulas for a class of degeneracy loci, which generalize Schubert varieties. The K-theoretic quiver formula of Buch expresses the structure sheaves of these loci as integral linear combinations of products of stable Grothendieck polynomials. We prove an explicit combinatorial formula for the coefficients, which shows that they have altern...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2004
ISSN: 0012-7094
DOI: 10.1215/s0012-7094-04-12214-6