Partition identities and quiver representations

par Anna Weigandt (University of Illinois, Urbana - Champaign)

mardi 24 janv. 2017, 10:45 → 11:45 Europe/Paris

Fokko du Cloux (ICJ)

We present a particular connection between classical partition combinatorics and the theory of quiver representations. Specifically, we give a bijective proof of an analogue of A. L. Cauchy's Durfee square identity to multipartitions. We then use this result to give a new proof of M. Reineke's identity in the case of quivers Q of Dynkin type A of arbitrary orientation. Our identity is stated in terms of the lacing diagrams of S. Abeasis - A. Del Fra, which parameterize orbits of the representation space of Q for a fixed dimension vector. This is joint work with R. Rimanyi and A. Yong.