Garnir relations and Dyck tilings

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• Matt Fayers, QMUL
• Wednesday 25 February 2015, 16:30-17:30
• MR12.

If you have a question about this talk, please contact David Stewart.

Recently the study of the representation theory of the symmetric group has been revolutionised by the discovery that the group algebra is isomorphic to a “cyclotomic quiver Hecke algebra”, which shows in particular that this algebra is graded. Kleshchev, Mathas and Ram have given a homogeneous presentation for any Specht module for the symmetric group. The relations in this presentation include ”homogeneous Garnir relations”, which appear in a slightly nebulous (and inefficient) form. I’ll describe what happens when the Garnir relations are re-written in terms of standard generators; as we’ll see, some interesting combinatorics related to Dyck tilings comes into play.

This talk is part of the Algebra and Representation Theory Seminar series.

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