Original scientific paper
The structure of the algebra \(\left (U(g)\otimes C(p) \right )^{K}\) for the groups \(SU(n,1)\) and \(SO_e(n,1)\)
Hrvoje Kraljević
orcid.org/0000-0002-8328-0815
; Depratment of Mathematics, University of Zagreb, Zagreb, Croatia
Abstract
The structure of the algebra of $K-$invariants in $\cU(\gg)\otim C(\pp)$ is important for constructing $(\gg,K)-$modules by means of algebraic Dirac induction as developed in [5] and its variants in [8] and [10]. We show that for the groups $\SU(n,1)$ and $\SO_e(n,1)$ this algebra is a free $\cU(\gg)^K-$module of rank $\dim C(\pp)=2^{\dim\pp}.$ We also indicate a way of constructing a $\cU(\gg)^K-$basis in $(\cU(\gg)\otim C(\pp))^K.$
Keywords
Universal enveloping algebra, Clifford algebra, Dirac operator, K-types, Kinvariants
Hrčak ID:
275678
URI
Publication date:
28.4.2022.
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