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Discrete Mathematics & Theoretical Computer Science |
Thomas Lam ; Aaron Lauve ; Frank Sottile - Skew Littlewood―Richardson rules from Hopf algebras
dmtcs:2853 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2853Skew Littlewood―Richardson rules from Hopf algebrasArticle
- 1 Department of Mathematics - University of Michigan
- 2 Department of Mathematics [Austin]
We use Hopf algebras to prove a version of the Littlewood―Richardson rule for skew Schur functions, which implies a conjecture of Assaf and McNamara. We also establish skew Littlewood―Richardson rules for Schur $P-$ and $Q-$functions and noncommutative ribbon Schur functions, as well as skew Pieri rules for k-Schur functions, dual k-Schur functions, and for the homology of the affine Grassmannian of the symplectic group.
Source: HAL:hal-01186281v1
Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: symmetric functions,Littlewood―Richardson rule,Pieri rule,Hopf algebras,antipode,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
- Source : OpenAIRE Graph
- Affine combinatorics, Schubert calculus, and total positivity; Funder: National Science Foundation; Code: 0901111
- FRG: Collaborative Research: Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects; Funder: National Science Foundation; Code: 0652641
- Applicable Algebraic Geometry: Real Solutions, Applications, and Combinatorics; Funder: National Science Foundation; Code: 0701050
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