This volume carries the same title as that of an international conference held at the National University of Singapore, 9–11 January 2006 on the occasion of Roger E. Howe’s 60th birthday. Authored by leading members of the Lie theory community, these contributions, expanded from invited lectures given at the conference, are a fitting tribute to the originality, depth and influence of Howe’s mathematical work. The range and diversity of the topics will appeal to a broad audience of research mathematicians and graduate students interested in symmetry and its profound applications.

Contents:

• The Theta Correspondence over ℝ (J Adams)
• The Heisenberg Group, SL(3, ℝ), and Rigidity (A Čap et al.)
• Pfaffians and Strategies for Integer Choice Games (R Evans & N Wallach)
• When is an L-Function Non-Vanishing in Part of the Critical Strip? (S Gelbart)
• Cohomological Automorphic Forms on Unitary Groups, II: Period Relations and Values of L-Functions (M Harris)
• The Inversion Formula and Holomorphic Extension of the Minimal Representation of the Conformal Group (T Kobayashi & G Mano)
• Classification des Séries Discrètes pour Certains Groupes Classiques p-Adiques (C Moeglin)
• Some Algebras of Essentially Compact Distributions of a Reductive p-Adic Group (A Moy & M Tadić)
• Annihilators of Generalized Verma Modules of the Scalar Type for Classical Lie Algebras (T Oshima)
• Branching to a Maximal Compact Subgroup (D A Vogan, Jr.)
• Small Semisimple Subalgebras of Semisimple Lie Algebras (J F Willenbring & G J Zuckerman)