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Analysis of the Brylinski-Kostant model for spherical minimal representations | | Dehbia Achab
; Jacques Faraut
; | | Date: |
23 Jan 2011 | | Abstract: | We revisit with another view point the construction by R. Brylinski and B.
Kostant of minimal representations of simple Lie groups. We start from a pair
$(V,Q)$, where $V$ is a complex vector space and $Q$ a homogeneous polynomial
of degree 4 on $V$. The manifold $Xi $ is an orbit of a covering of ${
m
Conf}(V,Q)$, the conformal group of the pair $(V,Q)$, in a finite dimensional
representation space. By a generalized Kantor-Koecher-Tits construction we
obtain a complex simple Lie algebra $goth g$, and furthermore a real form
${goth g}_{board R}$. The connected and simply connected Lie group
$G_{board R}$ with ${
m Lie}(G_{board R})={goth g}_{board R}$ acts
unitarily on a Hilbert space of holomorphic functions defined on the manifold
$Xi $ | | Source: | arXiv, 1101.4402 | | Services: | Forum | Review | PDF | Favorites | |
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