The connection between the strictly isospectral construction in supersymmetric quantum mechanics and the general zero mode solutions of the Schroedinger equation is explained by introducing slightly generalized first-order intertwining operators. We also present a multiple-parameter generalization of the strictly isospectral construction in the same perspective. PACS 03.65-Quantum mechanics.

We construct representations of the Cuntz algebra O3 from real cubic transformations on closed intervals. By intertwining relations of transformations, we have those of operators of representations of O2 and O3. By these relations, we show that such representations are unitarily equivalent to barycentric representations.

Free field representation of level-k(6 = 0,−2) Yangian double DY (sl2)k and a corresponding deformation of Wakimoto modules are presented. We also realize two types of vertex operators intertwining these modules. † Yukawa fellow ⋆ E-mail: [email protected]

Matrix elements of intertwining operators between q-Wakimoto modules associated to the tensor product of representations of Uq(c sl2) with arbitrary spins are studied. It is shown that they coincide with the Trasov-Varchenko’s formulae of the solutions of the qKZ equations. The result generalizes that of the previous paper [9].

We present a new method of calculating intertwining operators between principal series representations of semisimple Lie groups G. Working in the compact realization we nd the eigenvalues of the operators on the K-types, and give several examples. Among the advantages of our method is its applicability to bundle-valued cases. 0. Introduction Intertwining operators of various forms play an impor...

The connection between the strictly isospectral construction in supersymmetric quantum mechanics and the general zero mode solutions of the Schroedinger equation is explained by introducing slightly generalized first-order intertwining operators. We also present a multiple-parameter generalization of the strictly isospectral construction in the same perspective.