Highest Weight Theory for Finite W-Algebras

By Jonathan Brundan, Simon M. Goodwin, Alexander S. Kleshchev. 2008

82 citations recorded by the source corpus.

We define analogues of Verma modules for finite W-algebras. By the usual ideas of highest weight theory, this is a first step toward the classification of finite-dimensional irreducible modules. We also introduce an analogue of the BGG category . Motivated by known results in type A, we then formulate some precise conjectures in the case of nilpotent orbits of standard Levi type.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2aebcf37f42da3cceb6320809bc01d4211897128

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In Discrete Mathematics and Combinatorics

1. I. Losev
2. I. Gordon
3. Stephen Griffeth
4. Pavel Etingof
5. François Bergeron
6. Victor Reiner
7. Anne V. Shepler
8. S. Witherspoon

In Geometry and Topology

1. I. Gordon
2. I. Losev
3. V. Ginzburg
4. Pavel Etingof
5. Stephen Griffeth
6. E. Gorsky
7. T. Arakawa
8. A. Premet

In Mathematical Physics

1. I. Losev
2. I. Gordon
3. V. Ginzburg
4. Pavel Etingof
5. Stephen Griffeth
6. E. Gorsky
7. T. Arakawa
8. A. Premet

Citations in the corpus

• On category O for cyclotomic rational Cherednik algebras (2011, methodology): “The definition is inspired by the definition of the category Osph for W-algebras [13], [42], and for hypertoric varieties [10].”