Let K be a closed subgroup of U(n) acting on the (2n+ 1)dimensional Heisenberg group Hn by automorphisms. One calls (K,Hn) a Gelfand pair when the integrable K-invariant functions on Hn form a commutative algebra under convolution. We prove that this is the case if and only if the coadjoint orbits for G := K n Hn which meet the annihilator k⊥ of the Lie algebra k of K do so in single K-orbits. ...

Following Jiang Guanghao and Xu Luoshan’s concept of conjugative, dually conjugative, normal and dually normal relations on sets, the concept of quasi-regular relations is introduced. Characterizations of quasi-regular relations are obtained and it is shown when an anti-order relation is quasiregular. Some nontrivial examples of quasi-regular relations are given. At the end we introduce dually ...

In this work we prove that the set of points at infinity S8 :“ ClRPm pSqXH8 of a semialgebraic set S Ă R that is the image of a polynomial map f : R Ñ R is connected. This result is no longer true in general if f is a regular map. However, it still works for a large family of regular maps that we call quasi-polynomial maps.

We study quasi completely regular semirings through their congruence structures.