Results 1 to 10 of about 991 (39)
The puzzle conjecture for the cohomology of two-step flag manifolds [PDF]
Journal of Algebraic Combinatorics, 2016 We prove a conjecture of Knutson asserting that the Schubert structure constants of the cohomology ring of a two-step flag variety are equal to the number of puzzles with specified border labels that can be created using a list of eight puzzle pieces. As
Anders Skovsted Buch +2 more
exaly +3 more sources
Gromov-Witten invariants on Grassmannians [PDF]
, 2003 We prove that any three-point genus zero Gromov-Witten invariant on a type A Grassmannian is equal to a classical intersection number on a two-step flag variety. We also give symplectic and orthogonal analogues of this result; in these cases the two-step
Buch, Anders Skovsted +2 more
core +2 more sources
The Secant Conjecture in the real Schubert calculus [PDF]
, 2012 We formulate the Secant Conjecture, which is a generalization of the Shapiro Conjecture for Grassmannians. It asserts that an intersection of Schubert varieties in a Grassmannian is transverse with all points real, if the flags defining the Schubert ...
del Campo, Abraham Martin +6 more
core +4 more sources
Experimentation and conjectures in the real Schubert calculus for flag manifolds [PDF]
, 2005 The Shapiro conjecture in the real Schubert calculus, while likely true for Grassmannians, fails to hold for flag manifolds, but in a very interesting way.
Ruffo, James +3 more
core +2 more sources
A geometric Littlewood-Richardson rule [PDF]
, 2003 We describe an explicit geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties so that they break into Schubert varieties.
Vakil, Ravi
core +4 more sources
Quantum cohomology of the Lagrangian Grassmannian
, 2003 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
Kresch, Andrew, Tamvakis, Harry
core +1 more source
An update of quantum cohomology of homogeneous varieties [PDF]
, 2014 We describe recent progress on QH(G/P) with special emphasis of our own work.Comment: 18 pages.
Changzheng Li, Leung, Naichung Conan
core
Billey's formula in combinatorics, geometry, and topology [PDF]
, 2013 In this expository paper we describe a powerful combinatorial formula and its implications in geometry, topology, and algebra. This formula first appeared in the appendix of a book by Andersen, Jantzen, and Soergel.
Tymoczko, Julianna S.
core +2 more sources
A Pieri-type formula for isotropic flag manifolds
, 1998 We give the formula for multiplying a Schubert class on an odd orthogonal or symplectic flag manifold by a special Schubert class pulled back from a Grassmannian of maximal isotropic subspaces.
Bergeron, Nantel, Sottile, Frank
core +5 more sources
Pieri rules for the K-theory of cominuscule Grassmannians [PDF]
, 2010 We prove Pieri formulas for the multiplication with special Schubert classes in the K-theory of all cominuscule Grassmannians. For Grassmannians of type A this gives a new proof of a formula of Lenart. Our formula is new for Lagrangian Grassmannians, and
Anders Skovsted, Buch, Vijay Ravikumar
core +2 more sources