Open Access
Translator Disclaimer
2001 Descent-Cycling in Schubert Calculus
Allen Knutson
Experiment. Math. 10(3): 345-354 (2001).

Abstract

We prove two lemmata about Schubert calculus on generalized flag manifolds $G/B$, and in the case of the ordinary flag manifold $\GL_n/B$ we interpret them combinatorially in terms of descents, and geometrically in terms of missing subspaces. One of them gives a symmetry of Schubert calculus that we christen descent-cycling. Computer experiment shows these two lemmata are surprisingly powerful: they already suffice to determine all of $\GL_n$ Schubert calculus through $n=5$, and 99.97\%+ at $n=6$. We use them to give a quick proof of Monk's rule. The lemmata also hold in equivariant ("double'') Schubert calculus for Kac--Moody groups $G$.

Citation

Download Citation

Allen Knutson. "Descent-Cycling in Schubert Calculus." Experiment. Math. 10 (3) 345 - 354, 2001.

Information

Published: 2001
First available in Project Euclid: 25 November 2003

zbMATH: 1060.14078
MathSciNet: MR1917423

Rights: Copyright © 2001 A K Peters, Ltd.

JOURNAL ARTICLE
10 PAGES


SHARE
Vol.10 • No. 3 • 2001
Back to Top