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Stanley Symmetric Functions and Peterson Algebras

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k-Schur Functions and Affine Schubert Calculus

Part of the book series: Fields Institute Monographs ((FIM,volume 33))

Abstract

This purpose of this chapter is to introduce Stanley symmetric functions and affine Stanley symmetric functions from the combinatorial and algebraic point of view. The presentation roughly follows three lectures I gave at a conference titled “Affine Schubert Calculus” held in July of 2010 at the Fields Institute in Toronto.

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Notes

  1. 1.

    The author was supported by NSF grants DMS-0652641, DMS-0901111, and DMS-1160726, and by a Sloan Fellowship.

  2. 2.

    see http://www.fields.utoronto.ca/programs/scientific/10-11/schubert/

  3. 3.

    Our conventions differ from Stanley’s original definitions by \(w \leftrightarrow {w}^{-1}\).

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, USA

    Thomas Lam

  2. Instituto de Matemática y Física, Universidad de Talca, Talca, Chile

    Luc Lapointe

  3. Department of Mathematics, Drexel University, Philadelphia, PA, USA

    Jennifer Morse

  4. Department of Mathematics, University of California, Davis, CA, USA

    Anne Schilling

  5. Department of Mathematics, Virginia Tech, Blacksburg, VA, USA

    Mark Shimozono

  6. Mathematics and Statistics, York University, Toronto, ON, Canada

    Mike Zabrocki

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  4. Anne Schilling
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  5. Mark Shimozono
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  6. Mike Zabrocki
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Lam, T., Lapointe, L., Morse, J., Schilling, A., Shimozono, M., Zabrocki, M. (2014). Stanley Symmetric Functions and Peterson Algebras. In: k-Schur Functions and Affine Schubert Calculus. Fields Institute Monographs, vol 33. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0682-6_3

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