Journal of the Mathematical Society of Japan

The equivariant cohomology rings of Peterson varieties

Yukiko FUKUKAWA, Megumi HARADA, and Mikiya MASUDA

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Abstract

The main result of this note gives an efficient presentation of the $S^1$-equivariant cohomology ring of Peterson varieties (in type $A$) as a quotient of a polynomial ring by an ideal $J$, in the spirit of the well-known Borel presentation of the cohomology of the flag variety. Our result simplifies previous presentations given by Harada-Tymoczko and Bayegan-Harada. In particular, our result gives an affirmative answer to a conjecture of Bayegan and Harada that the defining ideal $J$ is generated by quadratics.

Article information

Source
J. Math. Soc. Japan, Volume 67, Number 3 (2015), 1147-1159.

Dates
First available in Project Euclid: 5 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1438777443

Digital Object Identifier
doi:10.2969/jmsj/06731147

Mathematical Reviews number (MathSciNet)
MR3376581

Zentralblatt MATH identifier
1339.55006

Subjects
Primary: 55N91: Equivariant homology and cohomology [See also 19L47]
Secondary: 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 14N15: Classical problems, Schubert calculus

Keywords
equivariant cohomology Peterson variety flag variety regular sequence

Citation

FUKUKAWA, Yukiko; HARADA, Megumi; MASUDA, Mikiya. The equivariant cohomology rings of Peterson varieties. J. Math. Soc. Japan 67 (2015), no. 3, 1147--1159. doi:10.2969/jmsj/06731147. https://projecteuclid.org/euclid.jmsj/1438777443


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References

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