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.

Matrix elements of intertwining operators between q-Wakimoto modules associated to the tensor product of representations of U q (sl 2) with arbitrary spins are studied. It is shown that they coincide with the Tarasov–Varchenko's formulae of the solutions of the qKZ equations. The result generalizes that of the previous paper [Kuroki K.

We describe a logarithmic tensor product theory for certain module categories for a “conformal vertex algebra.” In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not require the module categories to be semisimple, and we accommodate modules with generalized weight spaces. The corresponding intertwining operators contain logarithm...

In this paper, we study the asymptotic behavior of traces Hecke operators for spherical discrete automorphic representations fixed level on general split reductive groups over \(\mathbb {Q}\). Under a condition analytic intertwining operators, which is known classical and exceptional group \(G_2\), obtain expected asymptotics in terms Plancherel measure an explicit estimate remainder.

Intertwining relations for N -particle Calogero-like models with internal degrees of freedom are investigated. Starting from the well known Dunkl-Polychronakos operators, we construct new kind of local (without exchange operation) differential operators. These operators intertwine the matrix Hamiltonians corresponding to irreducible representations of the permutation group SN . In particular ca...