Maria Gorelik & Vladimir Hinich 
Representations and Nilpotent Orbits of Lie Algebraic Systems [PDF ebook] 
In Honour of the 75th Birthday of Tony Joseph

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.

Mục lục

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 Robinson‐Schensted Algorithm at Infinity.- Prime Spectra of Abelian 2-Categories and Categorifications of Richardson Varieties.