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Funktsional. Anal. i Prilozhen., 2008, Volume 42, Issue 1, Pages 53–62 (Mi faa2889)  

This article is cited in 1 scientific paper (total in 1 paper)

The PRV-Formula for Tensor Product Decompositions and Its Applications

D. I. Panyushev, O. S. Yakimova

Independent University of Moscow

Abstract: Let $G$ be a semisimple algebraic group, $V$ a simple finite-dimensional self-dual $G$-module, and $W$ an arbitrary simple finite-dimensional $G$-module. Using the triple multiplicity formula due to Parthasarathy, Ranga Rao, and Varadarajan, we describe the multiplicities of $W$ in the symmetric and exterior squares of $V$ in terms of the action of a maximum-length element of the Weyl group on some subspace in $V^T$, where $T\subset G$ is a maximal torus. By way of application, we consider the cases in which $V$ is the adjoint, little adjoint, or, more generally, a small $G$-module. We also obtain a general upper bound for triple multiplicities in terms of Kostant's partition function.

Keywords: semisimple Lie algebra, highest weight, triple multiplicity, partition function

DOI: https://doi.org/10.4213/faa2889

Full text: PDF file (218 kB)
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English version:
Functional Analysis and Its Applications, 2008, 42:1, 45–52

Bibliographic databases:

UDC: 512.745
Received: 25.04.2006

Citation: D. I. Panyushev, O. S. Yakimova, “The PRV-Formula for Tensor Product Decompositions and Its Applications”, Funktsional. Anal. i Prilozhen., 42:1 (2008), 53–62; Funct. Anal. Appl., 42:1 (2008), 45–52

Citation in format AMSBIB
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\by D.~I.~Panyushev, O.~S.~Yakimova
\paper The PRV-Formula for Tensor Product Decompositions and Its Applications
\jour Funktsional. Anal. i Prilozhen.
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\vol 42
\issue 1
\pages 53--62
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\transl
\jour Funct. Anal. Appl.
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\pages 45--52
\crossref{https://doi.org/10.1007/s10688-008-0005-7}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-41549139593}


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    This publication is cited in the following articles:
    1. Auger J., Lau M., “Extensions of Modules For Twisted Current Algebras”, J. Algebra, 526 (2019), 356–381  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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