Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Why should the Littlewood–Richardson Rule be true?
HTML articles powered by AMS MathViewer

by Roger Howe and Soo Teck Lee PDF
Bull. Amer. Math. Soc. 49 (2012), 187-236 Request permission

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
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
  • 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