This volume, a celebration of Anthony Joseph's fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled Algebraic Modes of Representations, the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including:

• Primitive ideals
• Invariant theory
• Geometry of Lie group actions
• Quantum affine algebras
• Yangians
• Categorification
• Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.

Commemorates the mathematical achievements of Anthony Joseph, one of Lie theory's leading figures Explores recent advances in topics that Joseph fundamentally influenced Equips readers with an understanding of various subjects within Lie algebra and representation theory

Inhalt
Preface.- Singular Support of a Vertex Algebra and the Arc Space of its Associated Scheme.- On Cacti and Crystals.- Quotients for Sheets of Conjugacy Classes.- About Polynomiality of the Poisson Semicentre for Parabolic Subalgebras.- On Dynkin Gradings in Simple Lie Algebras.- Multiplicative Slices, Relativistic Toda, and Shifted Quantum Affine Algebras.- Some Properties of Orbital Varieties in Extremal Nilpotent Orbits.- On Involutions in the Weyl Group and B-Orbit Closures in the Orthogonal Case.- Proper Self-Similar Triangle Tiling and Representing Weight Diagrams in the Plane.- Closures of On-Orbits in the Flag Variety for GLn.- On the Spin Calogero-Sutherland Model at Infinity.- Semi-Direct Products Involving Sp2n or Spinn with Free Algebras of Symmetric Invariants.- Primitive Ideals of U( sl ()) and The RobinsonSchensted Algorithm at Infinity.- Prime Spectra of Abelian 2-Categories and Categorifications of Richardson Varieties.