Cyclic Sieving Phenomenon of Plane Partitions and Cluster Duality of Grassmannian

Seminar: 
Arithmetic Algebraic Geometry
Event time: 
Monday, March 26, 2018 - 4:15pm to 5:15pm
Speaker: 
Daping Weng
Speaker affiliation: 
Yale University
Event description: 

Fix two positive integers a and b. Scott showed that a homogeneous coordinate ring of the Grassmannian Gra, a+b has the structure of a cluster algebra. This homogeneous coordinate ring can be decomposed into a direct sum of irreducible representations of GLa+b which correspond to integer multiples of the fundamental weight wa. By proving the Fock-Goncharov cluster duality conjecture for the Grassmannian using a sufficient condition found by Gross, Hacking, Keel, and Kontsevich, we obtain bases parametrized by plane partitions for these irreducible representations. As an application we use these bases to show a cyclic sieving phenomenon of plane partitions under a certain sequence of toggling operations. This is joint work with Jiuzu Hong and Linhui Shen.