Schubert polynomials for the affine Grassmannian
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- by Thomas Lam;
- J. Amer. Math. Soc. 21 (2008), 259-281
- DOI: https://doi.org/10.1090/S0894-0347-06-00553-4
- Published electronically: October 18, 2006
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Abstract:
Confirming a conjecture of Mark Shimozono, we identify polynomial representatives for the Schubert classes of the affine Grassmannian as the $k$-Schur functions in homology and affine Schur functions in cohomology. The results are obtained by connecting earlier combinatorial work of ours to certain subalgebras of Kostant and Kumar’s nilHecke ring and to work of Peterson on the homology of based loops on a compact group. As combinatorial corollaries, we settle a number of positivity conjectures concerning $k$-Schur functions, affine Stanley symmetric functions and cylindric Schur functions.References
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Bibliographic Information
- Thomas Lam
- Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
- MR Author ID: 679285
- ORCID: 0000-0003-2346-7685
- Email: tfylam@math.harvard.edu
- Received by editor(s): April 7, 2006
- Published electronically: October 18, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc. 21 (2008), 259-281
- MSC (2000): Primary 05E05; Secondary 14N15
- DOI: https://doi.org/10.1090/S0894-0347-06-00553-4
- MathSciNet review: 2350056