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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Catalan functions and $k$-Schur positivity
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by Jonah Blasiak, Jennifer Morse, Anna Pun and Daniel Summers PDF
J. Amer. Math. Soc. 32 (2019), 921-963 Request permission

Abstract:

We prove that graded $k$-Schur functions are $G$-equivariant Euler characteristics of vector bundles on the flag variety, settling a conjecture of Chen-Haiman. We expose a new miraculous shift invariance property of the graded $k$-Schur functions and resolve the Schur positivity and $k$-branching conjectures in the strongest possible terms by providing direct combinatorial formulas using strong marked tableaux.
References
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Additional Information
  • Jonah Blasiak
  • Affiliation: Department of Mathematics, Drexel University, Philadelphia, Pennsylvania 19104
  • MR Author ID: 763856
  • Email: jblasiak@gmail.com
  • Jennifer Morse
  • Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
  • MR Author ID: 640276
  • Email: morsej@virginia.edu
  • Anna Pun
  • Affiliation: Department of Mathematics, Drexel University, Philadelphia, Pennsylvania 19104
  • MR Author ID: 981492
  • Email: annapunying@gmail.com
  • Daniel Summers
  • Affiliation: Department of Mathematics, Drexel University, Philadelphia, Pennsylvania 19104
  • Email: danielsummers72@gmail.com
  • Received by editor(s): April 18, 2018
  • Received by editor(s) in revised form: January 31, 2019
  • Published electronically: August 22, 2019
  • Additional Notes: Authors were supported by NSF Grants DMS-1600391 (the first author) and DMS-1833333 (the second author)
  • © Copyright 2019 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 32 (2019), 921-963
  • MSC (2010): Primary 05E05, 05E10
  • DOI: https://doi.org/10.1090/jams/921
  • MathSciNet review: 4013737