NCSU Algebra and Combinatorics Seminar

This is the webpage for the NCSU Algebra and Combinatorics seminar, run by the NCSU Algebra and Combinatorics research group.

 

We typically meet Mondays from 3:00 pm - 4:00 pm. For the Spring 2021 semester, we will be meeting online with Zoom. If you would like to attend, please email Corey Jones at cmjones6@ncsu.edu to be added to the mailing list for weekly announcements of abstracts and Zoom links.

Below is a list of currently scheduled talks for this semester (which is updated regularly!):

Spring 2021:

2/29/2021- Corey Jones, North Carolina State University:

Symmetries of affine buildings and tilting modules for SL_n.

In this talk, we will explain a (mysterious?) connection between the combinatorics of affine buildings and representation theory in positive characteristic. If a group acts simply and transitively on the vertices of an affine building in type A_n, it gives rise to a certain combinatorial structure called a triangle presentation. We will describe how triangle presentations can be used to build exotic fiber functors on the category of tilting modules for SL_n (for n odd) in positive characteristic.

3/15/2021- Cris Negron, University of North Carolina, Chapel Hill: TBA

3/29/2021- Samantha Kirk, North Carolina State University: 

 

How to Construct Representations of Twisted Toroidal Lie Algebras via Lattice Vertex Algebras

If you take a simple finite-dimensional Lie algebra g and tensor it with the Laurent polynomials in one variable, then you will get an infinite-dimensional Lie algebra known as a loop algebra. Affine Lie algebras are the central extensions of such loop algebras and their representations have been of interest to several mathematicians. What happens if we tensor g with the Laurent polynomials in several variables (instead of just one) and create a central extension?  The result is known as a toroidal Lie algebra. I am interested in representations of certain toroidal Lie algebras that have been twisted. 

 

In this talk, I will show how representations of twisted toroidal Lie algebras can be constructed using lattice vertex algebras. The method I will use builds on what is known about the connection between lattice vertex algebras and representations of affine Lie algebras. In fact, the only difference is I will use a bigger lattice! This talk should be approachable for students who have taken MA 720 and/or MA 725.

 

(Joint work with Bojko Bakalov)

4/5/2021- Julia Plavnik, Indiana University: TBA

 

4/19/2021- GaYee Park, University of Massachusetts Amherst: TBA