Motivated by the work of Regge ([19, 20]) we are interested in the problem of recovering a radial potential in R from its resonance parameters, which are zeros of the appropriately defined Jost function. For a potential of compact support these may in turn be identified as the complex eigenvalues of a non-selfadjoint SturmLiouville problem with an eigenparameter dependent boundary condition. In...

The symmetric group S2n and the hyperoctaheadral group Hn is a Gelfand triple for an arbitrary linear representation φ of Hn. Their φ-spherical functions can be caught as transition matrix between suitable symmetric functions and the power sums. We generalize this triplet in the term of wreath product. It is shown that our triplet are always to be a Gelfand triple. Furthermore we study the rela...

A non-commutative version of the Bernštĕın-GelfandGelfand (BGG) correspondence is set up, and a sample application is given to periodic injective resolutions. 0. Introduction The Bernštĕın-Gelfand-Gelfand correspondence is surprising. It gives an equivalence of categories gr(E) ≃ D(coh P). This was proved in [4, thm. 2] and as always, to explain such a formula requires lots of words. On the lef...

In the (covariant) topos approach to quantum theory by Heunen, Landsman and Spitters, one associates to each unital C*-algebra A a topos T (A) of sheaves on a locale and a commutative C*-algebra A within that topos. The Gelfand spectrum of A is a locale Σ in this topos, which is equivalent to a bundle over the base locale. We further develop this external presentation of the locale Σ, by noting...

This work is part of a project on weight bases for the irreducible representations of semisimple Lie algebras with respect to which the representation matrices of the Chevalley generators are given by explicit formulas. In the case of sln, the celebrated Gelfand-Tsetlin basis is the only such basis known. Using the setup of supporting graphs developed by Donnelly, we present a new interpretatio...

We consider algebras over a field K presented by generators x1, . . . , xn and subject to (n 2 ) square-free relations of the form xixj = xkxl with every monomial xixj , i = j, appearing in one of the relations. It is shown that for n > 1 the Gelfand-Kirillov dimension of such an algebra is at least two if the algebra satisfies the so-called cyclic condition. It is known that this dimension is ...

A combinatorial construction of Gelfand models for the symmetric group, for its Iwahori-Hecke algebra and for the hyperoctahedral group is presented.