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Funktsional. Anal. i Prilozhen., 2004, Volume 38, Issue 4, Pages 22–35 (Mi faa124)  

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

Newton Polytopes, Increments, and Roots of Systems of Matrix Functions for Finite-Dimensional Representations

B. Ya. Kazarnovskii

Scientific Technical Centre "Informregistr"

Abstract: The asymptotic root distribution is computed for systems of matrix functions associated with finite-dimensional holomorphic representations of a Lie group. This distribution can be expressed via the increments of the representations involved. If the group is reductive, then the number of equations in the system can be arbitrary, from 1 to the dimension of the group. In this case, the computation results are stated in the language of convex geometry. These computations imply the previously known formulas for the density of the solution variety of a system of exponential equations as well as for the number of solutions of a polynomial system and, more generally, of a system formed by matrix functions of representations of a complex reductive Lie group.

Keywords: matrix function, increment, holomorphic representation, reductive Lie group, Lie algebra, current, asymptotic density, tropical ring, convex polytope

DOI: https://doi.org/10.4213/faa124

Full text: PDF file (236 kB)
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English version:
Functional Analysis and Its Applications, 2004, 38:4, 256–266

Bibliographic databases:

UDC: 512.7+514.172
Received: 05.07.2002

Citation: B. Ya. Kazarnovskii, “Newton Polytopes, Increments, and Roots of Systems of Matrix Functions for Finite-Dimensional Representations”, Funktsional. Anal. i Prilozhen., 38:4 (2004), 22–35; Funct. Anal. Appl., 38:4 (2004), 256–266

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. B. Ya. Kazarnovskii, ““Newton polyhedra” of distributions”, Izv. Math., 68:2 (2004), 273–289  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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