The classical Cartan-Helgason theorem characterises finite-dimensional
spherical representations of reductive Lie groups in terms of their highest
weights. We generalise the theorem to the case of a reductive symmetric
supergroup pair $(G,K)$ of even type. Along the way, we compute the
Harish-Chandra $c$-function of the symmetric superspace $G/K$. By way of an
application, we show that all spherical representations are self-dual in type
AIII|AIII.Comment: 37 pages; title changed; substantially revised version; accepted for
publication, J. Func. Anal. (2014
A homomorphic public key crypto-scheme based on the Boolean Satisfiability Problem is proposed. The public key is a SAT formula satisfied by the private key. Probabilistic encryption generates functions implied to be false by the public key XOR the message bits. A zero-knowledge proof is used to provide signatures.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.