Lie Group/Quantum Mathematics Seminar
Organizers Lisa Carbone, Yi-Zhi
Lepowsky and Siddhartha Sahi.
Time Friday, 12:00 am to 1:00 pm.
Place Hill 705.
Starting from Spring, 2008, the
Lie Group Seminar and Quantum Mathematics Seminar
have merged together to a single seminar called the
Lie Group/Quantum Mathematics
Seminar. This seminar also has a page
Lie Groups Quantum Mathematics Seminar,
maintained by email@example.com.
For the Lie Group/Quantum Mathematics seminar in previous
semesters, see this
For talks in the Quantum Mathematics Seminar from Spring, 1998 to
Fall, 2007, see
For the last few years, the Quantum Mathematics Seminar
shared the time and place with the Algebra Seminar.
For talks in both the Algebra and
Quantum Mathematics Seminars in the last few semesters, see the page
Seminar. For all the seminars and colloquia in the department, see
the Seminars and Colloquia page.
- Speaker Siddhartha Sahi, Rutgers University
- Title The Capelli eigenvalue problem for Lie
- Time/place 9/8/2017, Friday, 12:00 in Hill 705
- Abstract The Tits-Kantor-Koecher (TKK) construction attaches a simple Lie algebra to a simple Jordan algebra. In this setting one has a Jordan "norm" that generalizes the determinant, and a family of invariant differential operators generalizing the Capelli operators of classical invariant theory. In the early 1990s Bert Kostant and I studied the eigenvalues of these generalized Capelli operators, and a few years later Friedrich Knop and I discovered a surprising connection to Macdonald polynomials.
It turns out that these ideas have analogs for Lie superalgebras, although there are several subtle issues and new phenomena. I will describe a number of recent results in this direction, which have been obtained in joint work with Hadi Salmasian, Alexander Alldridge, and Vera Serganova.
- Speaker Sven Moeller, Rutgers University
- Speaker Bin Gui, Vanderbilt University
- Title A unitary tensor product theory for unitary
representations of unitary vertex operator algebras
- Time/place 9/22/2017, Friday, 12:00 in Hill 705
- Abstract A formal definition of unitary vertex operator algebras was introduced by Dong, Lin. For many examples of unitary VOAs (unitary minimal models, affine Lie algebras at non-negative integer levels), all representations are unitarizable. It is natural to ask whether their tensor product theories are unitary. In this talk, we try to answer this question. Let V be a unitary vertex operator algebra. We define a sesquilinear form on the tensor product of two unitary V-modules. We show that, when these sesquilinear forms are positive definite (i.e., when they are inner products), the modular tensor category for V is unitary. The positive definiteness of these sesquilinear forms, especially the positivity, is much harder to prove. We explain the main idea of the proof if time permitted.
- Speaker Fei Qi, Rutgers University
- Speaker Lisa Carbone, Rutgers University
- Title Groups for Borcherds algebras
- Time/place 10/13/2017, Friday, 12:00 in Hill 705
- Abstract Borcherds algebras are generalizations of Kac-Moody algebras and have wide applications in physical theories and the study of automorphic forms. We discuss the problem of associating the analog of a Lie a group to a Borcherds algebra and we present some examples, including the Monster Lie algebra.
- Speaker Jinwei Yang, Yale University
- Title Braided tensor categories of admissible
modules for affine Lie algebras
- Time/place 10/20/2017, Friday, 12:00 in Hill 705
- Abstract We construct a braided tensor category structure with a twist on a semisimple category of modules for an affine Lie algebra at an admissible level. We also prove the rigidity and modularity of this tensor category in the case of sl_2^. This is a joint work with T. Creutzig and Y.-Z. Huang.
- Speaker Alina Vdovina, University of Bath and Hunter College
- Title Buildings, surfaces and quaternions
- Time/place 12/1/2017, Friday, 12:00 in Hill 705
- Abstract Buildings are exciting objects which have geometric, algebraic
and number theoretical aspects. We will give elementary
constructions of several classes of buildings as universal
covers of finite complexes. Then (as a geometric application) we will show a connection of our results with Gromov's surface subgroup question and
(as an arithmetic application) we will give explicit examples of quaternionic lattices.
- Speaker Joseph Bernstein, Tel Aviv University and Institute for Advanced Study
- Title How to modify the Langlands' dual group
- Time/place 12/8/2017, Friday, 12:00 in Hill 705
- Abstract pdf file