Schur positivity of skew Schur function differences and
applications to ribbons and Schubert classes
Schur positivity of skew Schur function differences and
applications to ribbons and Schubert classes
Some new relations on skew Schur function differences are
established both combinatorially using Sch\"utzenberger's jeu de taquin, and algebraically using Jacobi-Trudi determinants. These relations lead to the conclusion that certain differences
of skew Schur functions are Schur positive. Applying these results to a basis of symmetric functions involving ribbon Schur functions confirms the validity of a Schur positivity conjecture due to McNamara. A further application reveals that certain differences of products of Schubert classes are Schubert positive.
jacobi-trudi determinant, jeu de taquin, ribbon, schubert calculus, schur positive, skew schur function, symmetric function
139-167
King, Ronald C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
Welsh, Trevor A.
3f6176e0-a8b3-4df3-92a3-99d543576db1
van Willigenberg, Stephanie J.
4d7889fa-bff4-4e94-a586-92ad32c79547
August 2008
King, Ronald C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
Welsh, Trevor A.
3f6176e0-a8b3-4df3-92a3-99d543576db1
van Willigenberg, Stephanie J.
4d7889fa-bff4-4e94-a586-92ad32c79547
King, Ronald C., Welsh, Trevor A. and van Willigenberg, Stephanie J.
(2008)
Schur positivity of skew Schur function differences and
applications to ribbons and Schubert classes.
Journal of Algebraic Combinatorics, 28, .
(doi:10.1007/s10801-007-0113-0).
Abstract
Some new relations on skew Schur function differences are
established both combinatorially using Sch\"utzenberger's jeu de taquin, and algebraically using Jacobi-Trudi determinants. These relations lead to the conclusion that certain differences
of skew Schur functions are Schur positive. Applying these results to a basis of symmetric functions involving ribbon Schur functions confirms the validity of a Schur positivity conjecture due to McNamara. A further application reveals that certain differences of products of Schubert classes are Schubert positive.
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Published date: August 2008
Keywords:
jacobi-trudi determinant, jeu de taquin, ribbon, schubert calculus, schur positive, skew schur function, symmetric function
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Local EPrints ID: 66210
URI: http://eprints.soton.ac.uk/id/eprint/66210
ISSN: 0925-9899
PURE UUID: 239e33bf-6c5b-4b0d-976a-111715fa8fac
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Date deposited: 12 Jan 2010
Last modified: 13 Mar 2024 18:13
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Contributors
Author:
Ronald C. King
Author:
Trevor A. Welsh
Author:
Stephanie J. van Willigenberg
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