Lie Groups, Lie Algebras and their Representations

(page last edited 25 April 2015)
The Lie Theory Workshop series of weekend conferences has been meeting several times a year since 1990.  Most years the NSF supports graduate students and postdoctoral participants, and the institution at which the workshop takes place also provides some support.  Most, but not all, of the workshops take place at West Coast universities.  Each workshop program is determined by the local organizers, and the workshop program itself is organized by a committee currently consisting of Geoff Mason (University of California, Santa Cruz)), Susan  Montgomery (University of Southern California) and Joseph Wolf (University of California at Berkeley).

The purpose of the program is to communicate results and ideas rather than to deliver polished presentations. The program also serves to acquaint graduate students in this area with a range of researchers in Lie theory and representation theory.  The next workshop is

   Spring 2015:  University of Alberta, Edmonton, May 16-17, 2015.  The local organizers are Arturo Pianzola ( and Terry Gannon (  The emphasis will be on geometric methods in Lie theory.
The tentative (25 April 2015) schedule is

Saturday May 16:
     9:30-10:30 Johannes Walcher (McGill)    Exponential networks and representations of quivers
                                 I will report on work in progress with Richard Eager and Sam
                                Selmani, in which we adapt some of the spectral network machinery of
                                Gaiotto-Moore-Neitzke to give a B-model description of the (known) BPS
                                spectrum of the simplest Calabi-Yau three-folds.

   11:00-12:00 Kai Behrend (UBC)               TBA
   12:00- 2:00 lunch
     2:00-3:00 Jon Brundan (Oregon)              Kac-Moody 2-categories
                                  I will review the definition of Kac-Moody 2-category due to Khovanov, Lauda
                                  and Rouquier. Then I will say something about their cyclotomic quotients

    3:15-3:45 Johanna Hennig (UCSD)          TBA
    4:00-4:30 Shashank Kanade (Rutgers)     The Rogers-Ramanujan identities: From sums, hopefully to products
                                  Feigin-Stoyanovsky's ``principal subspaces'' of level 1 standard
                                  modules for A_1^{(1)} exhibit the Rogers-Ramanujan ``sum sides,''
                                  i.e., the ``difference-2'' conditions as elegantly exhibited by
                                  Capparelli-Lepowsky-Milas and Calinescu-Lepowsky-Milas using
                                  vertex-operator-algebraic methods.  In this talk, we will discuss some
                                  ideas and results for using vertex-operator-theoretic techniques to
                                  interpret the corresponding ``product sides.'' To this end, stimulated
                                  by an idea of J. Lepowsky, we present some results on a certain Koszul
                                  complex related to the principal subspaces.  The underlying
                                  constructions are surprisingly ubiquitous and arise in various
                                  settings, for instance, in Gorsky-Oblomkov-Rasmussen's analysis of the
                                  Khovanov homology of torus knots.  Further work on this problem is in
                                  progress with J. Lepowsky and S. Sahi.

    4.45-5.15 Jie Sun (Western Michigan U)  TBA.
Sunday May 17:
   9:30-10:30 David Evans (Cardiff)              TBA
  11:00-12:00 Thomas Creutzig (Alberta)      Coset Vertex Algebras
                                The coset construction is one of the very few methods to obtain a new
                                vertex algebra out of a given one. The main example is the sub algebra of
                                an affine vertex algebra associated to some Lie super algebra commuting
                                with an affine sub algebra. Unfortunately, there are few general statements
                                available (but many conjectures). I will explain why such coset vertex
                                algebras are generically strongly finitely generated. Then I will present
                                results concerning a Schur-Weyl type duality including modules that are not
                                completely reducible as well as examples.

The schedule will be updated as the information on titles and abstracts becomes available.

The local airport is Edmonton International (YEG). There are several ways to get to the university/hotels from the airport:
--  shuttle:   $30 return (= round trip) (you must pre-book)
--  taxi (approx $55 one way), no need to pre-book
--  public transportation  (approx $3 one way, 45 minutes to university from airport, but leaves once an hour)

The hotel closest to the university (Campus Towers) is on the edge of campus, 5 minute walk from the Math department, where all the talks will be held.   Rooms at Campus Towers (with university discount) costs approximately $150 per night. A cheaper alternative is Lister Hall (student residences), which will be empty in May: rooms there cost something like $50 if you are willing to share a bathroom with another person (BIRS style), or $70 for a room with its own bathroom.  Just now we're waiting for updated information on cost/availability.  If you want to just go ahead on your own on this, the contact information on Lister Hall is

          Lister Hall Guest Services*Phone: (780) 492-6056
          Fax: (780) 492-5597


Conference participants who desire funding from the NSF must fly on a US carrier and must be based in the U.S.  We will not be able to obtain any exceptions to these NSF requirements.

The Government of Canada has recently instituted NEW ENTRY REGULATIONS for some visitors to Canada.   If you have neither Canadian citizenship nor landed immigrant status, then the conference local organizers can supply a letter formally inviting you to the conference. For this you would have to write to one of the local organizers to request the letter of invitation.  These new regulations don't require any further effort or cost to the participants, but don't forget to bring the letter of invitation!  For U.S. citizens or permanent residents it is less complicated if you bring appropriate documentation; see ,   or .


Winter 2015:  University of California, Riverside, February 14-15, 2015.  The local organizers were Jacob Greenstein (,  Vyjayanthi Chari ( and Carl Mautner.  The emphasis was on representation theory.  The list of speakers includes Achar, Dobrovolska, Friedlander, Lauda, Loseu, Pevtsova, Rosso, Yun and Zhu.  The conference web site is

The Fall 2014 workshop took place at the  University of Washington (Seattle), November 15-16, 2014.  The local organizer was James Zhang and the emphasis will be on Hopf algebras and actions.

The Spring 2014 workshop took place at the University of Southern California (USC), May 19-22, 2014, local organizers were Aravind Asok, Robert Guralnick, Aaron Lauda and Susan Montgomery .  The conference was joint with a conference in celebration of the 70th birthday of Eric Friedlander.  The Friedlander conference web site is

The Winter 2014 workshop took place at Stanford University, February 1-2.  The local organizers were Apoorva Khare, Daniel Bump and Persi Diaconis. 
The Fall 2013 workshop took place at the University of California, Berkeley, October 12-13.  The local organizer was Joseph Wolf (

The Spring 2013 workshop took place at the University of Oregon, April 27-28.  The local organizer was Jon Brundan (  The emphasis was on tensor categories and categorification.

The Winter 2013 workshop in the program took place at the University of California San Diego (UCSD), January 19-20.  The local organizers were Alireza Salehi Golsefidy, Daniel Rogalski and Efim Zelmanov.  The emphasis was on Lie groups and related areas.

The Fall 2012 workshop took place at Louisiana State University, October 6-7.  The local organizers were Gestur Olafsson and Milen Yakimov.  The emphasis was on  Representation theory and analysis on homogeneous spaces.

The Spring 2012 workshop took place at the University of Southern California (USC), May 5-6.  The local organizers were Susan Montgomery and  Miodrag Iovanov.  The emphasis was on  Hopf algebras and related areas.

The Winter 2012 workshop took place at Stanford University.  The local organizers were Apoorva Khare, Daniel Bump and Anne Schilling.  The emphasis was on Quantum Groups and related areas.