Maximal Newton Points and the Quantum Bruhat Graph
نویسندگان
چکیده
We discuss a surprising relationship between the partially ordered set of Newton points associated with an affine Schubert cell and quantum cohomology complex flag variety. The main theorem provides combinatorial formula for unique maximum element in this poset terms paths Bruhat graph, whose vertices are indexed by elements finite Weyl group. Key to establishing connection is fact that graph encode saturated chains strong order on This correspondence also fundamental work Lam Shimozono Peterson’s isomorphism variety homology Grassmannian. One important geometric application present inequality which necessary condition nonemptiness certain Deligne–Lusztig varieties
منابع مشابه
Quantum Bruhat Graph and Schubert Polynomials
The quantum Bruhat graph, which is an extension of the graph formed by covering relations in the Bruhat order, is naturally related to the quantum cohomology ring of G/B. We enhance a result of Fulton and Woodward by showing that the minimal monomial in the quantum parameters that occurs in the quantum product of two Schubert classes has a simple interpretation in terms of directed paths in thi...
متن کاملun 2 00 2 QUANTUM BRUHAT GRAPH AND SCHUBERT POLYNOMIALS
The quantum Bruhat graph, which is an extension of the graph formed by covering relations in the Bruhat order, is naturally related to the quantum cohomology ring of G/B. We enhance a result of Fulton and Wood-ward by showing that the minimal monomial in the quantum parameters that occurs in the quantum product of two Schubert classes has a simple interpretation in terms of directed paths in th...
متن کاملLine graphs associated to the maximal graph
Let $R$ be a commutative ring with identity. Let $G(R)$ denote the maximal graph associated to $R$, i.e., $G(R)$ is a graph with vertices as the elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$ containing both. Let $Gamma(R)$ denote the restriction of $G(R)$ to non-unit elements of $R$. In this paper we study the various graphi...
متن کاملMaximal nests of subspaces, the matrix Bruhat decomposition, and the marriage theorem - with an application to graph coloring
Using the celebrated Marriage Theorem of P. Hall, we give an elementary combinatorial proof of the theorem that asserts that given two maximal nests N1 and N2 in a finite dimensional vector space V , there is an ordered basis of V that generates N1 and a permutation of that ordered basis that generates N2. From this theorem one easily obtains the Matrix Bruhat Decomposition. A generalization to...
متن کاملMaximal degree in the Strong Bruhat Order of Bn
Given a permutation π ∈ Sn, let Γ−(π) be the graph on n vertices {1, . . . , n} where two vertices i < j are adjacent if π(i) > π(j) and there are no integers k, i < k < j, such that π(i) > π(k) > π(j). Let Γ(π) be the graph obtained by dropping the condition that π(i) > π(j), i.e. two vertices are adjacent if the rectangle [i, π(i)] × [j, π(j)] is empty. In the study of the strong order on per...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2021
ISSN: ['0026-2285', '1945-2365']
DOI: https://doi.org/10.1307/mmj/20175356