This volume is an outgrowth of the activities of the RIMS Research Project, which presented symposia offering both individual lectures on specialized topics and expository courses on current research. The subjects therein reflect very active areas in the representation theory of Lie groups. Also included are various topical interactions with geometry of homogeneous spaces, automorphic forms, quantum groups, special functions, discrete groups, differential equations, etc. Comprising results from some of today's most active areas of research, this volume will serve as an excellent up-to-date guide to the representation theory of Lie groups.
Characters of non-linear groups by J. Adams Selberg's eigenvalue conjecture and the Siegel zeros for Hecke $L$-series by E. Balslev and A. Venkov Proprietes asymptotiques des groupes lineaires (II) by Y. Benoist Matrix coefficients of the principal $P j$-series and the middle discrete series of $SU(2,2)$ by T. Hayata, H. Koseki, and T. Oda $K$-type structure in the principal series of $GL 3$, I by R. Howe Discretely decomposable restrictions of unitary representations of reductive Lie groups--examples and conjectures by T. Kobayashi On $\wedge\mathfrak g$ for a semisimple Lie algebra $\mathfrak g$, as an equivariant module over the symmetric algebra $S(\mathfrak g)$ by B. Kostant Tilting modules and their applications by O. Mathieu On the theta lift for the trivial representation by E.-C. Tan Hypergeometric systems and Radon transforms for Hermitian symmetric spaces by T. Tanisaki Orbits on homogeneous spaces of arithmetic origin and approximations by G. Tomanov A Langlands classification for unitary representations by D. A. Vogan, Jr. Modular transformation of twisted characters of admissible representations and fusion algebras associated to non-symmetric transformation matrices by M. Wakimoto Symposia.