arXiv subjects

Masaki Nakagawa

Publications and source records attributed to Masaki Nakagawa.

22 records · Page 2Linked to original sources

arXiv2010

The Chow rings of the algebraic groups E_6, E_7, and E_8

We determine the Chow rings of the complex algebraic groups of the exceptional type E_6, E_7, and E_8, giving the explicit generators represented by the pull-back images of Schubert varieties of the corresponding flag varieties. This is a continuation of the work of R. Marlin on the computation of the Chow rings of SO_n, Spin_n, G_2, and F_4. Our method is based on Schubert calculus of the corresponding flag varieties, which has its own interest.

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arXiv2010

The integral cohomology ring of E_8/T

We give a complete description of the integral cohomology ring of the flag manifold E_8/T, where E_8 denotes the compact exceptional Lie group of rank 8 and T its maximal torus, by the method due to Borel and Toda. This completes the computation of the integral cohomology rings of the flag manifolds for all compact connected simple Lie groups.

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arXiv2009

The integral cohomology ring of E_8/T^1E_7

We determine the integral cohomology ring of the homogeneous space E_8/T^1E_7 by the Borel presentation and a method due to Toda. Then using the Gysin exact sequence associated with the circle bundle S^1 -> E_8/E_7 -> E_8/T^1E_7, we also determine the integral cohomology of E_8/E_7.

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arXiv2008

A description based on Schubert classes of cohomology of flag manifolds

We describe the integral cohomology rings of the flag manifolds of types B_n, D_n, G_2 and F_4 in terms of their Schubert classes. The main tool is the divided difference operators of Bernstein-Gelfand-Gelfand and Demazure. As an application, we compute the Chow rings of the corresponding complex algebraic groups, recovering thereby the results of R. Marlin.

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