Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

Why should the Littlewood-Richardson Rule be true?


Authors: Roger Howe and Soo Teck Lee
Journal: Bull. Amer. Math. Soc. 49 (2012), 187-236
MSC (2000): Primary 20G05; Secondary 05E15
Published electronically: October 20, 2011
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 20G05, 05E15

Retrieve articles in all journals with MSC (2000): 20G05, 05E15


Additional Information

Roger Howe
Affiliation: Department of Mathematics, Yale University, New Haven, Connecticut 06520-8283
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

DOI: http://dx.doi.org/10.1090/S0273-0979-2011-01358-1
PII: S 0273-0979(2011)01358-1
Keywords: Littlewood-Richardson Rule, Pieri Rule, $GL_{n}$ tensor product algebra, $(GL_{n}, GL_{m})$-duality.
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.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.