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Izv. RAN. Ser. Mat., 2004, Volume 68, Issue 2, Pages 159–190 (Mi izv479)  

This article is cited in 3 scientific papers (total in 3 papers)

The intermediate Lie algebra $\mathfrak d_{n-1/2}$, the weight scheme and finite-dimensional representations with highest weight

V. V. Shtepin


Abstract: Multiple points of the spectrum in the reduction $D_n\downarrow D_{n-1}$ are separated by introducing a non-semisimple intermediate subalgebra and a weight scheme different from the Gel'fand–Tsetlin scheme. We suggest a method of constructing a weight basis in the space of a finite-dimensional irreducible representation of $D_n$. The elements of this basis are labelled by such weight schemes. We also study the category of finite-dimensional highest-weight representations of this intermediate Lie algebra.

DOI: https://doi.org/10.4213/im479

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English version:
Izvestiya: Mathematics, 2004, 68:2, 375–404

Bibliographic databases:

UDC: 519.46
MSC: 17E10, 22E46
Received: 20.08.2002

Citation: V. V. Shtepin, “The intermediate Lie algebra $\mathfrak d_{n-1/2}$, the weight scheme and finite-dimensional representations with highest weight”, Izv. RAN. Ser. Mat., 68:2 (2004), 159–190; Izv. Math., 68:2 (2004), 375–404

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. A. A. Zorin, “Action of the centralizer of a co-isotropic subalgebra on an irreducible representation of a simple Lie algebra”, Russian Math. Surveys, 63:6 (2008), 1156–1158  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. V. V. Shtepin, T. V. Shtepina, “An application of intertwining operators in functional analysis”, Izv. Math., 73:6 (2009), 1265–1288  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. V. V. Shtepin, D. L. Konashenkov, “Characters and dimensions of highest-weight representations of the intermediate Lie group $D_{n-1/2}$”, Izv. Math., 78:3 (2014), 621–639  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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