CU Algebraic Lie Theory Seminar

Counting Quiver Representations over Finite Fields

Geir Helleloid, University of Texas at Austin

March 17, 2009
2-3pm
Math 220

Abstract

In 2000, Hua gave a (complicated) formula for the number of isomorphism classes of absolutely indecomposable representations of a quiver over the finite field F_q with a fixed dimension vector. This number is a polynomial in q with integer coefficients (the coefficients are conjecturally non-negative). After introducing quiver representations and Hua's formula, I will discuss joint work with Fernando Rodriguez-Villegas in which we extract information from Hua's formula. In this work, we see connections to the enumeration of certain graphs and derivatives of q-binomial coefficients.