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The Schubert calculus

2010
An enumerative problem asks the following type of question; how many figures (lines, planes, conies, cubics, etc.) meet transversely (or are tangent to) a certain number of other figures in general position? The last century saw the development of a calculus for solving this problem and a large number of examples were worked out by Schubert, after whom
openaire   +1 more source

Affine Schubert Calculus

2014
This chapter discusses how k-Schur and dual k-Schur functions can be defined for all types. This is done via some combinatorial problems that come from the geometry of a very large family of generalized flag varieties. They apply to the expansion of products of Schur functions, k-Schur functions and their dual basis, and Schubert polynomials.
Thomas Lam   +5 more
openaire   +1 more source

An arithmetic Schubert calculus

1995
Let \({\mathbb{G}}(n,p)\) be the Grassmann variety of \(p\)-dimensional subspaces of an \(n\)-dimensional space over \(\text{Spec } \mathbb{Z}\). It is shown that the Chow-Arakelov ring of \({\mathbb{G}}(n,p)\) is isomorphic to the ring \({\mathcal A}(p,n)\), where \({\mathcal A}(p,n)\) is defined as follows.
openaire   +2 more sources

Schubert calculus and the Hopf algebra structures of exceptional Lie groups

Forum Mathematicum, 2014
Xuezhi Zhao, Haibao Duan
exaly  

Schubert Calculus and Its Applications in Combinatorics and Representation Theory

Springer Proceedings in Mathematics and Statistics, 2020
exaly  

Schubert calculus and singularity theory

Journal of Geometry and Physics, 2012
Vassily Gorbounov, Victor Petrov
exaly  

Quantum and affine Schubert calculus and Macdonald polynomials

Advances in Mathematics, 2017
Avinash Dalal, Jennifer Morse
exaly  

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