Why should the Littlewood–Richardson Rule be true?
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- by Roger Howe and Soo Teck Lee PDF
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Abstract:
We give a proof of the Littlewood-Richardson Rule for describing tensor products of irreducible finite-dimensional representations of $\textrm {GL}_n$. The core of the argument uses classical invariant theory, especially $(\textrm {GL}_n, \textrm {GL}_m)$-duality. Both of the main conditions (semistandard condition, lattice permutation/Yamanouchi word condition) placed on the tableaux used to define Littlewood-Richardson coefficients have natural interpretations in the argument.References
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Additional Information
- Roger Howe
- Affiliation: Department of Mathematics, Yale University, New Haven, Connecticut 06520-8283
- MR Author ID: 88860
- ORCID: 0000-0002-5788-0972
- Email: howe@math.yale.edu
- Soo Teck Lee
- Affiliation: Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076, Singapore
- Email: matleest@nus.edu.sg
- Received by editor(s): March 30, 2009
- Received by editor(s) in revised form: February 14, 2011
- Published electronically: October 20, 2011
- Additional Notes: The second named author is partially supported by NUS grant R-146-000-110-112.
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Bull. Amer. Math. Soc. 49 (2012), 187-236
- MSC (2000): Primary 20G05; Secondary 05E15
- DOI: https://doi.org/10.1090/S0273-0979-2011-01358-1
- MathSciNet review: 2888167