A combinatorial rule for (co)minuscule Schubert calculus
By Hugh Thomas, Alexander Yong. 2006
78 citations recorded by the source corpus.
We prove a root system uniform, concise combinatorial rule for Schubert calculus of minuscule and cominuscule flag manifolds G/P (the latter are also known as compact Hermitian symmetric spaces). We connect this geometry to the poset combinatorics of Proctor, thereby giving a generalization of Schutzenberger's jeu de taquin formulation of the Littlewood–Richardson rule that computes the intersection numbers of Grassmannian Schubert varieties. Our proof introduces cominuscule recursions, a general technique to relate the numbers for different Lie types.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/19b69959d37df4a6f26bcc73cfaf3b1b65159ceb
How researchers see this paper
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In Algebra and Number Theory
- Matthew J. Samuel
- Anders Skovsted Buch
- N. Perrin
- P. Chaput
- Hugh Thomas
- Laurent Manivel
- Alexander Yong
- I. Reiten
In Discrete Mathematics and Combinatorics
- P. Chaput
- N. Perrin
- Alexander Yong
- Anders Skovsted Buch
- Hugh Thomas
- Matthew J. Samuel
- Laurent Manivel
- Leonardo Constantin Mihalcea
In Mathematical Physics
- Alexander Yong
- Matthew J. Samuel
- Hugh Thomas
- Anders Skovsted Buch
- P. Chaput
- N. Perrin
- Laurent Manivel
- Damir Yeliussizov
Citations in the corpus
- Quantum Cohomology of Minuscule Homogeneous Spaces (2006, methodology): “shape of Diagram 5 which rectify after jeu de Taquin to the tableau of Diagram 6 (we use the same denitions as in [ TY ]).”
- A jeu de taquin theory for increasing tableaux, with applications to K-theoretic Schubert calculus (2007, methodology): “Briefly, using the ideascontained in this paper, together with those in [ ThYo06 , ThYo07a] it is not hard to show that KjdtG/P;{xi} is well-defined.”
- K-theory of minuscule varieties (2013, methodology): “We remark that there are other ways to identify ΛX with a subset of N (2), and the choices made in Table 2 are slightly different from those made in [27].”
- On the quantum cohomology of adjoint varieties (2009, background): “(ii) The geometry of minuscule homogeneous varieties is better understood than the geometry of general homogeneous spaces (see, for example, [29, 31] or [27]).”