On products of sln characters and support containment

Galyna Dobrovolska, Pavlo Pylyavskyy

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Let λ, μ, ν and ρ be dominant weights of sln satisfying λ + μ = ν + ρ. Let Vλ denote the highest weight module corresponding to λ. Lam, Postnikov, Pylyavskyy conjectured a sufficient condition for Vλ ⊗ Vμ to be contained in Vν ⊗ Vρ as sln-modules. In this note we prove a weaker version of the conjecture. Namely we prove that under the conjectured conditions every irreducible sln-module which appears in the decomposition of Vλ ⊗ Vμ does appear in the decomposition of Vν ⊗ Vρ.

Original languageEnglish (US)
Pages (from-to)706-714
Number of pages9
JournalJournal of Algebra
Volume316
Issue number2
DOIs
StatePublished - Oct 15 2007

Bibliographical note

Funding Information:
✩ The research was funded by SPUR program at MIT. * Corresponding author. E-mail addresses: galyna@mit.edu (G. Dobrovolska), pasha@math.mit.edu, pylyavskyy@gmail.com (P. Pylyavskyy).

Keywords

  • Horn-Klyachko inequalities
  • Schur functions

Fingerprint Dive into the research topics of 'On products of sl<sub>n</sub> characters and support containment'. Together they form a unique fingerprint.

Cite this