[PDF][PDF] Models for irreducible representations of Spin (m)
P Van Lancker, F Sommen… - Advances in applied …, 2001 - biblio.ugent.be
P Van Lancker, F Sommen, D Constales
Advances in applied Clifford algebras, 2001•biblio.ugent.be… This leads to the idea to look for models of half integer weight irreducible representations
of Spin(m) inside spaces of monogenic functions of several vector variables. This theory
was already developed to some extent in [Co] (in the case of several quaternionic variables
see eg [ABLSS], [Pa] and [Pe]). As a matter of fact, to obtain polynomial irreducible
representations of Spin(m) we look to spaces of polynomials which are already irreducible
with respect to the action of GL(m). These are the so called simplicial polynomials or …
of Spin(m) inside spaces of monogenic functions of several vector variables. This theory
was already developed to some extent in [Co] (in the case of several quaternionic variables
see eg [ABLSS], [Pa] and [Pe]). As a matter of fact, to obtain polynomial irreducible
representations of Spin(m) we look to spaces of polynomials which are already irreducible
with respect to the action of GL(m). These are the so called simplicial polynomials or …
Abstract
In this paper we consider harmonic and monogenic polynomials of simplicial type. It is proved that these polynomials provide explicit realizations of all irreducible representations of Spin (m).
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