W‑algebras learning seminar

University of Toronto

Winter 2012

Organisers
Joel Kamnitzer
Stephen Morgan
Daniel Rowe
Time
Wednesdays, 16:00 – 18:00
Place
Bahen 6180
Subject matter
This is a learning seminar on the subject of W‑algebras and their relation to nilpotent orbits. We shall primarily follow Wang's lecture notes on the subject ([W]).
Date Speaker Topic References
08 Feb Chris Dodd An introduction to and motivation for W‑algebras [W] [GG] [L1] [P]
15 Feb Daniel Rowe The Harish-Chandra isomorphism, the associated variety and nilpotent orbits [G] [CG]
22 Feb Reading week, no seminar
29 Feb¹ Jaimal Thind Symplectic resolutions, their deformations and quantisations [K] [BPW] [CG]
07 Mar Zsuzsanna Dancsó sl₂-triples, good gradings and Slodowy slices [W] [GG]
14 Mar Oded Yacobi Quantisation of Slodowy slices, quantum Hamiltonian reduction and the BRST definition of W‑algebras [GG] [W]
21 Mar Daniel Rowe The Skryabin equivalence, Whittaker modules and Kostant's theorem [W] [L2]
28 Mar Stephen Morgan Losev's theorem [L1] [L2]
04 Apr Stephen Morgan, Chris Dodd Losev's theorem continued [L1] [L2]
Onward To be determined
  1. Time moved to 16:30

References

[W]
Weiqiang Wang, Nilpotent orbits and finite W‑algebras, Fields institute communication series 59 (2011), pp. 70 – 105, arXiv:0912.0689 [math.RT]
[BPW]
Tom Braden, Nicholas Proudfoot and Ben Webster, Quantizations of conical symplectic resolutions I: local and global structure (Preprint)
[CG]
Neil Chriss and Victor Ginzburg, Representation theory and complex geometry, (Boston: Birkhäuser, 1997)
[GG]
Wee Liang Gan and Victor Ginzburg, Quantization of Slodowy slices, arXiv:math/0105225 [math.RT]
[G]
Victor Ginzburg, On primitive ideals, arXiv:math/0202079 [math.RT]
[K]
Dmitry Kaledin, Geometry and toploogy of symplectic resolutions, arXiv:math/0608143 [math.AG]
[L1]
Ivan Losev, Finite dimensional representations of W‑algebras, Duke Math J. 159 (2011), n. 1, pp. 99 – 143, arXiv:0807.1023 [math.RT]
[L2]
Ivan Losev, Finite W‑algebras, arXiv:1003.5811 [math.RT]
[P]
Alexander Premet, Enveloping algebras of Slodowy slices and the Joseph ideal, arXiv:math/0504343 [math.RT]