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Errata to ``Totally positive Toeplitz matrices and quantum cohomology of partial flag varieties''


Author: Konstanze Rietsch
Journal: J. Amer. Math. Soc. 21 (2008), 611-614
MSC (2000): Primary 20G20, 15A48, 14N35, 14N15
DOI: https://doi.org/10.1090/S0894-0347-07-00580-2
Published electronically: November 7, 2007
Original Article: J. Amer. Math. Soc. 16 (2003), 363-392.
MathSciNet review: 2373362
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Abstract | References | Similar Articles | Additional Information

Abstract: We make a correction to Remark 4.3 and the proof of Theorem 4.2 (Peterson's Theorem) which identifies $ qH^*(SL_n/P)$ with the coordinate ring $ \mathcal O(\mathcal Y_P)$ of a certain affine stratum of the Peterson variety $ \mathcal Y$. Explicitly, we introduce additional coordinates to obtain a complete coordinate system on $ B^+w_P B^-/B^-$ and then show that they lie in the defining ideal of the Peterson variety $ \mathcal Y_P$, hence play no role in the presentation of $ \mathcal O(\mathcal Y_P)$.


References [Enhancements On Off] (What's this?)

  • [33] D. Peterson, Quantum cohomology of $ {G}/{P}$, Lecture Course, M.I.T., Spring Term, 1997.
  • [35] K. Rietsch, Quantum cohomology of Grassmannians and total positivity, Duke Math. J. 113 (2001), no. 3, 521-551. MR 1869115 (2003c:14063)
  • [38] -, Totally positive Toeplitz matrices and quantum cohomology of partial flag varieties, J. Amer. Math. Soc. 16 (2003), 363-392. MR 1949164 (2004d:14081)

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Additional Information

Konstanze Rietsch
Affiliation: Department of Mathematics, King’s College London, Strand, London WC2R 2LS, United Kingdom
Email: konstanze.rietsch@kcl.ac.uk

DOI: https://doi.org/10.1090/S0894-0347-07-00580-2
Keywords: Flag varieties, quantum cohomology
Received by editor(s): September 23, 2005
Published electronically: November 7, 2007
Additional Notes: During the writing of this errata article the author was funded by a Royal Society Dorothy Hodgkin Research Fellowship and was visiting the University of Waterloo, Canada.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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