Author:
Lam Thomas,Lee Seung Jin,Shimozono Mark
Abstract
We study the back stable Schubert calculus of the infinite flag variety. Our main results are:
–a formula for back stable (double) Schubert classes expressing them in terms of a symmetric function part and a finite part;–a novel definition of double and triple Stanley symmetric functions;–a proof of the positivity of double Edelman–Greene coefficients generalizing the results of Edelman–Greene and Lascoux–Schützenberger;–the definition of a new class of bumpless pipedreams, giving new formulae for double Schubert polynomials, back stable double Schubert polynomials, and a new form of the Edelman–Greene insertion algorithm;–the construction of the Peterson subalgebra of the infinite nilHecke algebra, extending work of Peterson in the affine case;–equivariant Pieri rules for the homology of the infinite Grassmannian;–homology divided difference operators that create the equivariant homology Schubert classes of the infinite Grassmannian.
Subject
Algebra and Number Theory
Reference52 articles.
1. KL15 Knutson, A. and Lederer, M. , A $K_T$ -deformation of the ring of symmetric functions, Preprint (2015), arXiv:1503.04070.
2. Representations of quantum groups at a $p$-th root of unity and of semisimple groups in characteristic $p$: independence of $p$;Andersen;Astérisque,1994
3. Schubert polynomials for the affine Grassmannian
4. Factorial supersymmetric Schur functions and super Capelli identities
Cited by
30 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献