Representations of Reductive Groups

Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups. His groundbreaking ideas have lead to deep advances in the theory of real and p-adic groups, and have forged lasting connections with other subjects, including number theory, automorphic forms, algebraic geometry, and combinatorics.

Representations of Reductive Groups is an outgrowth of the conference of the same name, dedicated to David Vogan on his 60th birthday, which took place at MIT on May 19-23, 2014. This volume highlights the depth and breadth of Vogan's influence over the subjects mentioned above, and point to many exciting new directions that remain to be explored. Notably, the first article by McGovern and Trapa offers an overview of Vogan's body of work, placing his ideas in a historical context.

Contributors: Pramod N. Achar, Jeffrey D. Adams, Dan Barbasch, Manjul Bhargava, Cédric Bonnafé, Dan Ciubotaru, Meinolf Geck, William Graham, Benedict H. Gross, Xuhua He, Jing-Song Huang, Toshiyuki Kobayashi, Bertram Kostant, Wenjing Li, George Lusztig, Eric Marberg, William M. McGovern, Wilfried Schmid, Kari Vilonen, Diana Shelstad, Peter E. Trapa, David A. Vogan, Jr. , Nolan R. Wallach, Xiaoheng Wang, Geordie Williamson

Preface. - McGovern, Trapa, The Mathematical Work of David A. Vogan, Jr. - Achar, On Exotic and Perverse-Coherent Sheaves. - Adams, Vogan, Jr. , Parameters for Twisted Representations. - Barbasch, Ciubotaru, Ladder Representations of GL (
n
, Q
_p
). - Bhargava, Gross, Wang, Arithmetic Invariant Theory II: Pure Inner Forms and Obstructions to the Existence of Orbits. - Bonnafé, Geck, Hecke Algebras with Unequal Parameters and Vogan' s Left Cell Invariants. - Graham, Li, The Smooth Loci of Spiral Schubert Varieties of Type A
₂
. - He, Centers and Cocenters of 0-Hecke Algebras. - Huang, Dirac Cohomology, Elliptic Representations, and Endoscopy. - Kobayashi, A Program for Branching Problems in the Representation Theory of Real Reductive Groups. - Kostant, Equations for a Filtration of Sheets and The Variety of Singular Elements of a Complex Semisimple Lie Algebra. - Lusztig, On Conjugacy Classes in a Reductive Group. - Lusztig, Vogan, Jr. , Hecke Algebras and Involutions in Coxeter Groups. - Marberg, Comparing and Characterizing some Constructions of Canonical Bases from Coxeter Groups. - McGovern, Upper Semicontinuity of KLV Polynomials for Certain Blocks of Harish-Chandra Modules. - Schmid, Vilonen, Hodge Theory and Unitary Representations, in the Example of SL(2, R). - Shelstad, On Elliptic Factors in Real Endoscopic Transfer I. - Wallach, On the Gelfand-Kirillov Dimension of a Discrete Series Representation. - Williamson, A Reducible Characteristic Variety in Type A.