Grobner geometry of Schubert polynomials

• 成果类型: Article
• 署名作者: Knutson, A; Miller, E
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2005.161.1245
• 发表日期: 2005
• 页码: 1245-1318
• 关键词: differential-operators; homogeneous spaces; ladder; VARIETIES; rings; loci; complexes; FORMULA; bases; krs

摘要

Given a permutation w is an element of S-n, we consider a determinantal ideal I-w whose generators are certain minors in the generic n x n matrix (filled with independent variables). Using 'multidegrees' as simple algebraic substitutes for torus-equivariant cohomology classes on vector spaces, our main theorems describe, for each ideal I-w: variously graded multidegrees and Hilbert series in terms of ordinary and double Schubert and Grothendieck polynomials; a Grobner basis consisting of minors in the generic n x n matrix; the Stanley-Reisner simplicial complex of the initial ideal in terms of known combinatorial diagrams [FK96], [BB93] associated to permutations in Sn; and a procedure inductive on weak Bruhat order for listing the facets of this complex.