In this talk, we will explain a (mysterious?) connection between the combinatorics of affine buildings and representation theory in type A. 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…

We consider a finite group scheme G, and its associated representation category rep G.  Here one can think of a finite discrete group, or an infinitesimal group scheme, such as the kernel of the r-th Frobenius map for GL_n over F_p.  Via a standard tensor categorical construction one has Drinfeld's center Z(rep G) of the…

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…