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.

Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS.

Readership

Graduate students and research mathematicians interested in Lie groups and their representations.

Table of Contents

• J. Adams -- Characters of non-linear groups
• E. Balslev and A. Venkov -- Selberg's eigenvalue conjecture and the Siegel zeros for Hecke $L$-series
• Y. Benoist -- Propriétés asymptotiques des groupes linéaires (II)
• T. Hayata, H. Koseki, and T. Oda -- Matrix coefficients of the principal $P_j$-series and the middle discrete series of $SU(2,2)$
• R. Howe -- $K$-type structure in the principal series of $GL_3$, I
• T. Kobayashi -- Discretely decomposable restrictions of unitary representations of reductive Lie groups--examples and conjectures
• B. Kostant -- On $\wedge\mathfrak g$ for a semisimple Lie algebra $\mathfrak g$, as an equivariant module over the symmetric algebra $S(\mathfrak g)$
• O. Mathieu -- Tilting modules and their applications
• E.-C. Tan -- On the theta lift for the trivial representation
• T. Tanisaki -- Hypergeometric systems and Radon transforms for Hermitian symmetric spaces
• G. Tomanov -- Orbits on homogeneous spaces of arithmetic origin and approximations
• D. A. Vogan, Jr. -- A Langlands classification for unitary representations
• M. Wakimoto -- Modular transformation of twisted characters of admissible representations and fusion algebras associated to non-symmetric transformation matrices
• Symposia