# 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.