Studies in Lie Theory

Dedicated to Anthony Joseph in honor of his 60th birthday, this volume contains two articles reviewing different aspects of Joseph's impact on the theory of representations of Lie algebras and 17 original contributions from leading specialists in the field. The book contains new results on different aspects of Lie theory, including Lie superalgebras, quantum groups, crystal bases, representations of reductive groups in finite characteristic, and the geometric Langlands program.

Survey and Review. - The work of Anthony Joseph in classical representation theory. - Quantized representation theory following Joseph. - Research Articles. - Opérateurs différentiels invariants et problème de Noether. - Langlands parameters for Heisenberg modules. - Instanton counting via affine Lie algebras II: From Whittaker vectors to the Seiberg-Witten prepotential. - Irreducibility of perfect representations of double affine Hecke algebras. - Algebraic groups over a 2-dimensional local field: Some further constructions. - Modules with a Demazure flag. - Microlocalization of ind-sheaves. - Endoscopic decomposition of certain depth zero representations. - Odd family algebras. - Gelfand-Zeitlin theory from the perspective of classical mechanics. I. - Extensions of algebraic groups. - Differential operators and cohomology groups on the basic affine space. - A q-analogue of an identity of N. Wallach. - Centralizers in the quantum plane algebra. - Centralizer construction of the Yangian of the queer Lie superalgebra. - Definitio nova algebroidis verticiani.