The Terwilliger algebra of an almost-bipartite P- and Q-polynomial association scheme

Let $Y$ denote a $D$-class symmetric association scheme with $D \geq 3$, and suppose $Y$ is almost-bipartite P- and Q-polynomial. Let $x$ denote a vertex of $Y$ and let $T=T(x)$ denote the corresponding Terwilliger algebra. We prove that any irreducible $T$-module $W$ is both thin and dual thin in the sense of Terwilliger. We produce two bases for $W$ and describe the action of $T$ on these bases. We prove that the isomorphism class of $W$ as a $T$-module is determined by two parameters, the dual endpoint and diameter of $W$. We find a recurrence which gives the multiplicities with which the irreducible $T$-modules occur in the standard module. We compute this multiplicity for those irreducible $T$-modules which have diameter at least $D-3$.Comment: 22 page

Spin effects in nucleon‐nucleon elastic scattering

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87693/2/54_1.pd

Hadron beams session‐summary

The status of presently operating polarized beams at Fermilab, the AGS, and KEK is discussed. Other schemes such as Siberian Snakes and self−polarization of a beam in situ are briefly analyzed.(AIP)Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87382/2/1048_1.pd

Early strong interaction counter experiments

The 17 ° beam and some π‐p two body scattering experiments run in the beginning years of the ZGS are discussed. (AIP)Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87620/2/70_1.pd

Spin measurements in hadronic high momentum transfer scattering

The results of recent experiments investigating spin effects in hadronic high momentum transfer scattering are reviewed. There is evidence for very large spin dependences at high momentum transfer in measurements involving both the polarization of a single particle and the polarizations of two particles.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87596/2/521_1.pd

A family of tridiagonal pairs and related symmetric functions

A family of tridiagonal pairs which appear in the context of quantum integrable systems is studied in details. The corresponding eigenvalue sequences, eigenspaces and the block tridiagonal structure of their matrix realizations with respect the dual eigenbasis are described. The overlap functions between the two dual basis are shown to satisfy a coupled system of recurrence relations and a set of discrete second-order $q-$difference equations which generalize the ones associated with the Askey-Wilson orthogonal polynomials with a discrete argument. Normalizing the fundamental solution to unity, the hierarchy of solutions are rational functions of one discrete argument, explicitly derived in some simplest examples. The weight function which ensures the orthogonality of the system of rational functions defined on a discrete real support is given.Comment: 17 pages; LaTeX file with amssymb. v2: few minor changes, to appear in J.Phys.A; v3: Minor misprints, eq. (48) and orthogonality condition corrected compared to published versio