Let (W,S) be a Coxeter system, let S = I ∪ J be a partition of S such that no element of I is conjugate to an element of J , let J̃ be the set of WI -conjugates of elements of J and let W̃ be the subgroup of W generated by J̃ . We show that W = W̃ ⋊WI and that J̃ is the canonical set of Coxeter generators of the reflection subgroup W̃ of W . We also provide algebraic and geometric conditions for an e...

We study the general geometrical structure of the coadjoint orbits of a semidirect product formed by a Lie group and a representation of this group on a vector space. The use of symplectic induction methods gives new insight into the structure of these orbits. In fact, each coadjoint orbit of such a group is obtained by symplectic induction on some coadjoint orbit of a " smaller " Lie group. We...

in this paper we introduce two-wavelet constants for square integrable representations of homogeneous spaces. we establishthe orthogonality relations for square integrable representationsof homogeneous spaces which give rise to the existence of aunique self adjoint positive operator on the set of admissiblewavelets. finally, we show that this operator is a constant multiple of identity operator...

Consider the semidirect product group H ×? K, where H and K are two arbitrary locally compact groups and K is also abelian. We introduce the continuous wavelet transform associated to some square integrable representations H ×? K. Moreover, we try to obtain a concrete form for admissible vectors of these integrable representations.

In this paper we describe $${\mathcal {R}}$$ -unipotent semigroups being regular extensions of a left band by an $$\mathcal {R}$$ semigroup T as certain subsemigroups wreath product T. We obtain Szendrei’s result that each E-unitary is embeddable into semidirect group. Further, specialising the first author’s notion $$\lambda $$ -semidirect locally semigroup, provide answer to open question rai...

We prove necessary conditions for a commutative Banach algebra to be the semidirect product of some subalgebra together with a speci ed principal ideal. x