location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword Jordan algebra

 Expand all        Collapse all Results 1 - 2 of 2

1. CJM 2012 (vol 64 pp. 721)

Achab, Dehbia; Faraut, Jacques
 Analysis of the Brylinski-Kostant Model for Spherical Minimal Representations 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 ${\rm Conf}(V,Q)$, 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 $\mathfrak g$, and furthermore a real form ${\mathfrak g}_{\mathbb R}$. The connected and simply connected Lie group $G_{\mathbb R}$ with ${\rm Lie}(G_{\mathbb R})={\mathfrak g}_{\mathbb R}$ acts unitarily on a Hilbert space of holomorphic functions defined on the manifold $\Xi$. Keywords:minimal representation, Kantor-Koecher-Tits construction, Jordan algebra, Bernstein identity, Meijer $G$-functionCategories:17C36, 22E46, 32M15, 33C80

2. CJM 2006 (vol 58 pp. 3)

Ben Saïd, Salem
 The Functional Equation of Zeta Distributions Associated With Non-Euclidean Jordan Algebras This paper is devoted to the study of certain zeta distributions associated with simple non-Euclidean Jordan algebras. An explicit form of the corresponding functional equation and Bernstein-type identities is obtained. Keywords:Zeta distributions, functional equations, Bernstein polynomials, non-Euclidean Jordan algebrasCategories:11M41, 17C20, 11S90
 top of page | contact us | privacy | site map |