Skip to Main Content

Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

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.

 

Lowest $\mathfrak {sl}(2)$-types in $\mathfrak {sl}(n)$-representations
HTML articles powered by AMS MathViewer

by Hassan Lhou and Jeb F. Willenbring
Represent. Theory 21 (2017), 20-34
DOI: https://doi.org/10.1090/ert/492
Published electronically: March 13, 2017

Abstract:

Fix $n \geq 3$. Let $\mathfrak {s}$ be a principally embedded $\mathfrak {sl}_2$-subalgebra in $\mathfrak {sl}_n$. A special case of results of the second author and Gregg Zuckerman implies that there exists a positive integer $b(n)$ such that for any finite dimensional irreducible $\mathfrak {sl}_n$-representation, $V$, there exists an irreducible $\mathfrak {s}$-representation embedding in $V$ with dimension at most $b(n)$. We prove that $b(n)=n$ is the sharpest possible bound. We also address embeddings other than the principal one.

The exposition involves an application of the Cartan–Helgason theorem, Pieri rules, Hermite reciprocity, and a calculation in the “branching algebra” introduced by Roger Howe, Eng-Chye Tan, and the second author.

References
Similar Articles
  • Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 17B10, 05E10, 22E46
  • Retrieve articles in all journals with MSC (2010): 17B10, 05E10, 22E46
Bibliographic Information
  • Hassan Lhou
  • Affiliation: Department of Mathematical Sciences, University of Wisconsin - Milwaukee, 3200 North Cramer Street, Milwaukee, Wisconsin 53211
  • Email: hlhou@uwm.edu
  • Jeb F. Willenbring
  • Affiliation: Department of Mathematical Sciences, University of Wisconsin - Milwaukee, 3200 North Cramer Street, Milwaukee, Wisconsin 53211
  • MR Author ID: 662347
  • Email: jw@uwm.edu
  • Received by editor(s): September 12, 2016
  • Received by editor(s) in revised form: October 23, 2016
  • Published electronically: March 13, 2017
  • Additional Notes: The second author was supported by the National Security Agency grant # H98230-09-0054.
  • © Copyright 2017 American Mathematical Society
  • Journal: Represent. Theory 21 (2017), 20-34
  • MSC (2010): Primary 17B10; Secondary 05E10, 22E46
  • DOI: https://doi.org/10.1090/ert/492
  • MathSciNet review: 3622114