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Representations of Reductive Groups: In Honor of the 60th Birthday of David A. Vogan, Jr.

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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

Author(s): Monica Nevins, Peter E. Trapa
Series: Progress in Mathematics
Publisher: Birkhäuser
Year: 2016

Language: English
Pages: 545
Tags: Topological Groups, Lie Groups; Algebraic Geometry; Number Theory

Front Matter....Pages i-xix
The Mathematical Work of David A. Vogan, Jr.....Pages 1-10
On exotic and perverse-coherent sheaves....Pages 11-49
Parameters for twisted representations....Pages 51-116
Ladder representations of \(\mathrm{GL}(n, \mathbb{Q}_{p})\) ....Pages 117-137
Arithmetic invariant theory II: Pure inner forms and obstructions to the existence of orbits....Pages 139-171
Hecke algebras with unequal parameters and Vogan’s left cell invariants....Pages 173-187
The smooth loci of spiral Schubert varieties of type \(\widetilde{A}_{2}\) ....Pages 189-226
Centers and cocenters of 0-Hecke algebras....Pages 227-240
Dirac cohomology, elliptic representations and endoscopy....Pages 241-276
A program for branching problems in the representation theory of real reductive groups....Pages 277-322
Equations for a filtration of sheets and the variety of singular elements of a complex semisimple Lie algebra....Pages 323-332
On conjugacy classes in a reductive group....Pages 333-363
Hecke algebras and involutions in Coxeter groups....Pages 365-398
Comparing and characterizing some constructions of canonical bases from Coxeter systems....Pages 399-436
Upper semicontinuity of KLV polynomials for certain blocks of Harish-Chandra modules....Pages 437-441
Hodge theory and unitary representations....Pages 443-453
On elliptic factors in real endoscopic transfer I....Pages 455-504
On the Gelfand–Kirillov dimension of a discrete series representation....Pages 505-516
A reducible characteristic variety in type A ....Pages 517-532