International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2006 / Article

Open Access

Volume 2006 |Article ID 086494 | https://doi.org/10.1155/IJMMS/2006/86494

Cenap Özel, Erol Yilmaz, "Combinatorial integers (m,nj) and Schubert calculus in the integral cohomology ring of infinite smooth flag manifolds", International Journal of Mathematics and Mathematical Sciences, vol. 2006, Article ID 086494, 55 pages, 2006. https://doi.org/10.1155/IJMMS/2006/86494

Combinatorial integers (m,nj) and Schubert calculus in the integral cohomology ring of infinite smooth flag manifolds

Received18 Jul 2005
Revised22 Feb 2006
Accepted25 Apr 2006
Published31 Aug 2006

Abstract

We discuss the calculation of integral cohomology ring of LG/T and ΩG. First we describe the root system and Weyl group of LG, then we give some homotopy equivalences on the loop groups and homogeneous spaces, and calculate the cohomology ring structures of LG/T and ΩG for affine group A^2. We introduce combinatorial integers (m,nj) which play a crucial role in our calculations and give some interesting identities among these integers. Last we calculate generators for ideals and rank of each module of graded integral cohomology algebra in the local coefficient ring [1/2].

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Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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