# A tale of two staircases

Algebra/Geometry/Topology Seminar

#### by Kevin Purbhoo

Institution: Waterloo
Date: Fri 9th November 2012
Time: 3:15 PM
Location: 213 Richard Berry

Abstract: The number of standard Young tableaux of "staircase" shape $$(n,n-1,..., 2, 1)$$ is $$2^{n(n-1)/2}$$ times the number of standard Young tableaux of the corresponding shifted staircase shape. This can be proved in a number of ways; I will mainly talk about a bijective proof. The bijection is simple to state --- the trouble is it's far from obvious that it actually does the right thing. The fact that it works can be deduced from the existence of a certain embedding of the Lagrangian Grassmannian with some surprising properties.