Developments and Retrospectives in Lie Theory

1. Front Matter

   Pages i-x

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2. Group Gradings on Lie Algebras, with Applications to Geometry. I

   • Yuri Bahturin, Michel Goze, Elisabeth Remm

   Pages 1-50

3. Bounding the Dimensions of Rational Cohomology Groups

   • Christopher P. Bendel, Brian D. Boe, Christopher M. Drupieski, Daniel K. Nakano, Brian J. Parshall, Cornelius Pillen et al.

   Pages 51-69

4. Representations of the General Linear Lie Superalgebra in the BGG Category \(\mathcal{O}\)

   • Jonathan Brundan

   Pages 71-98

5. Three Results on Representations of Mackey Lie Algebras

   • Alexandru Chirvasitu

   Pages 99-109

6. Free Field Realizations of the Date-Jimbo-Kashiwara-Miwa Algebra

   • Ben Cox, Vyacheslav Futorny, Renato Alessandro Martins

   Pages 111-136

7. The Deformation Complex is a Homotopy Invariant of a Homotopy Algebra

   • Vasily Dolgushev, Thomas Willwacher

   Pages 137-158

8. Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities

   • Michael Eastwood, Alexander Isaev

   Pages 159-173

9. Generalized Loop Modules for Affine Kac–Moody Algebras

   • Vyacheslav Futorny, Iryna Kashuba

   Pages 175-183

10. Twisted Localization of Weight Modules

    • Dimitar Grantcharov

    Pages 185-206

11. Dirac Cohomology and Generalization of Classical Branching Rules

    • Jing-Song Huang

    Pages 207-228

12. Cleft Extensions and Quotients of Twisted Quantum Doubles

    • Geoffrey Mason, Siu-Hung Ng

    Pages 229-246

13. On the Structure of \(\mathbb{N}\)-Graded Vertex Operator Algebras

    • Geoffrey Mason, Gaywalee Yamskulna

    Pages 247-274

14. Variations on a Casselman–Osborne Theme

    • Dragan Miličić

    Pages 275-289

15. Tensor Representations of Mackey Lie Algebras and Their Dense Subalgebras

    • Ivan Penkov, Vera Serganova

    Pages 291-330

16. Algebraic Methods in the Theory of Generalized Harish-Chandra Modules

    • Ivan Penkov, Gregg Zuckerman

    Pages 331-350

17. On Exceptional Vertex Operator (Super) Algebras

    • Michael P. Tuite, Hoang Dinh Van

    Pages 351-384

18. The Cubic, the Quartic, and the Exceptional Group G2

    • Anthony van Groningen, Jeb F. Willenbring

    Pages 385-397

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades. These workshops have been sponsored by the NSF, noting the talks have been seminal in describing new perspectives in the field covering broad areas of current research. At the beginning, the top universities in California and Utah hosted the meetings which continue to run on a quarterly basis. Experts in representation theory/Lie theory from various parts of the US, Europe, Asia (China, Japan, Singapore, Russia), Canada, and South and Central America were routinely invited to give talks at these meetings. Nowadays, the workshops are also hosted at universities in Louisiana, Virginia, and Oklahoma. The contributors to this volume have all participated in these Lie theory workshops and include in this volume expository articles which cover representation theory from the algebraic, geometric, analytic, and topological perspectives with also important connections to math physics. These survey articles, review and update the prominent seminal series of workshops in representation/Lie theory mentioned-above, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, number theory, and mathematical physics. Many of the contributors have had prominent roles in both the classical and modern developments of Lie theory and its applications.

• Kazhdan-Lusztig conjectures
• differential geometry
• harmonic analysis
• mathematical physics
• representation theory
• superalgebras

• Department of Mathematics, University of California, Santa Cruz, Santa Cruz, USA

  Geoffrey Mason

• Jacobs University, Bremen, Germany

  Ivan Penkov

• Department of Mathematics, University of California, Berkeley, Berkeley, USA

  Joseph A. Wolf

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