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Transactions of the American Mathematical Society Series B

Published by the American Mathematical Society since 2014, this gold open access electronic-only journal is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 2330-0000

The 2024 MCQ for Transactions of the American Mathematical Society Series B is 1.73.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An equivariant basis for the cohomology of Springer fibers
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by Martha Precup and Edward Richmond;
Trans. Amer. Math. Soc. Ser. B 8 (2021), 481-509
DOI: https://doi.org/10.1090/btran/57
Published electronically: June 10, 2021

Abstract:

Springer fibers are subvarieties of the flag variety that play an important role in combinatorics and geometric representation theory. In this paper, we analyze the equivariant cohomology of Springer fibers for $GL_n(\mathbb {C})$ using results of Kumar and Procesi that describe this equivariant cohomology as a quotient ring. We define a basis for the equivariant cohomology of a Springer fiber, generalizing a monomial basis of the ordinary cohomology defined by De Concini and Procesi and studied by Garsia and Procesi. Our construction yields a combinatorial framework with which to study the equivariant and ordinary cohomology rings of Springer fibers. As an application, we identify an explicit collection of (equivariant) Schubert classes whose images in the (equivariant) cohomology ring of a given Springer fiber form a basis.
References
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Bibliographic Information
  • Martha Precup
  • Affiliation: Department of Mathematics and Statistics, Washington University in St. Louis, St. Louis, Missouri 63130
  • MR Author ID: 1043988
  • Email: martha.precup@wustl.edu
  • Edward Richmond
  • Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma , 74078
  • MR Author ID: 875224
  • Email: edward.richmond@okstate.edu
  • Received by editor(s): February 4, 2020
  • Received by editor(s) in revised form: August 14, 2020
  • Published electronically: June 10, 2021
  • Additional Notes: The first author was supported by an Oklahoma State University CAS summer research grant. The second author was partially supported by an AWM-NSF travel grant and NSF grant DMS 1954001 during the course of this research.
  • © Copyright 2021 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
  • Journal: Trans. Amer. Math. Soc. Ser. B 8 (2021), 481-509
  • MSC (2020): Primary 05E10, 14M15; Secondary 14N15
  • DOI: https://doi.org/10.1090/btran/57
  • MathSciNet review: 4273195