This article is cited in 2 papers

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.

UDC: 519.46

MSC: 22E47, 17B10, 22E60

Received: 11.07.2012

DOI: 10.4213/im8034

 English version: Izvestiya: Mathematics, 2014, 78:3, 621–639

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