We consider a reductive dual pair (G,G′) in the stable range with G′ the smaller member and of Hermitian symmetric type. We study the theta lifting of nilpotent K ′ C-orbits, where K ′ is a maximal compact subgroup of G′ and we describe the precise KC-module structure of the regular function ring of the closure of the lifted nilpotent orbit of the symmetric pair (G,K). As an application, we pro...

In this note, we prove that the projective normality of (P(V )/G,L), the celebrated theorem of Erdös-Ginzburg-Ziv and normality of an affine semigroup are all equivalent, where V is a finite dimensional representation of a finite cyclic group G over C and L is the descent of the line bundle O(1)⊗|G|.

between-subjects (groups) factor A with j=1,...,p levels and nj observations at each j and a single within-subjects (occasions) factor B with k=1,...,q levels is very frequent in almost all scientific fields (Shoukri & Pause, 1999). Although the nature of these designs is typically multivariate, the effects of design (occasions main effect and groups x occasions interaction) can be tested by us...

This note presents three ways of constructing simultaneous condence intervals for linear estimates of linear functionals in inverse problems, including \Backus-Gilbert" estimates. Simultaneous con dence intervals are needed to compare estimates, for example, to nd spatial variations in a distributed parameter. The notion of simultaneous con dence intervals is introduced using coin tossing as an...

This paper is devoted to the algebraic and combinatorial properties of polytopal semigroup rings defined as follows. Let P be a lattice polytope in R n , i. e. a poly-tope whose vertices have integral coordinates, and K a field. Then one considers the embedding ι : R n → R n+1 , ι(x) = (x, 1), and defines S P to be the semigroup generated by the lattice points in ι(P); the K-algebra K[S P ] is ...