By Thomas Lam,Luc Lapointe,Jennifer Morse,Anne Schilling,Mark Shimozono,Mike Zabrocki
This ebook offers an advent to the very energetic box of combinatorics of affine Schubert calculus, explains the present state-of-the-art, and states the present open difficulties. Affine Schubert calculus lies on the crossroads of combinatorics, geometry, and illustration conception. Its smooth improvement is prompted by way of likely unrelated instructions. One is the advent of k-Schur services within the learn of Macdonald polynomial positivity, a quite often combinatorial department of symmetric functionality idea. the opposite path is the examine of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formula of an issue in enumerative geometry.
This is the 1st introductory textual content in this topic. It includes many examples in Sage, a loose open resource normal objective mathematical software program procedure, to appeal to the reader to enquire the open difficulties. This e-book is written for complicated undergraduate and graduate scholars, in addition to researchers, who are looking to get to grips with this interesting new field.
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k-Schur Functions and Affine Schubert Calculus (Fields Institute Monographs) by Thomas Lam,Luc Lapointe,Jennifer Morse,Anne Schilling,Mark Shimozono,Mike Zabrocki