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Izv. RAN. Ser. Mat., 2014, Volume 78, Issue 3, Pages 205–224 (Mi izv8034)  

Characters and dimensions of highest-weight representations of the intermediate Lie group $D_{n-1/2}$

V. V. Shtepin, D. L. Konashenkov

Donetsk National University

Abstract: We study highest-weight representations of the non-semisimple complex Lie group $D_{n-1/2}$ used for separating multiple points of the spectrum in the reduction $D_n\downarrow D_{n-1}$. In particular, we find formulae for the characters and dimensions of these representations, which turn out to be similar to the well-known Weyl formulae for classical Lie groups.

Keywords: semiclassical intermediate Lie groups, finite-dimensional highest-weight representations, branching rules, weight basis, character and dimension of a representation of a Lie group.

DOI: https://doi.org/10.4213/im8034

Full text: PDF file (612 kB)
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English version:
Izvestiya: Mathematics, 2014, 78:3, 621–639

Bibliographic databases:

UDC: 519.46
MSC: 22E47, 17B10, 22E60
Received: 11.07.2012

Citation: V. V. Shtepin, D. L. Konashenkov, “Characters and dimensions of highest-weight representations of the intermediate Lie group $D_{n-1/2}$”, Izv. RAN. Ser. Mat., 78:3 (2014), 205–224; Izv. Math., 78:3 (2014), 621–639

Citation in format AMSBIB
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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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