Title:  Affine sl(n) crystals and cylindric partitions
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Abstract:  Various fundamental questions in Lie theory concern characters of
irreducible representations and decompositions of tensor products.
Kashiwara's theory of crystals gives a nice combinatorial approach to
such classical questions. I will begin by explaining Kashiwara's
crystals, mainly using the example of sl(3), and without assuming
prior knowledge of Lie theory. I will then discuss the case I am most
interested in; crystals for affine sl(n) (the loop algebra of sl(n)).
This leads to combinatorics involving cylindric partitions (and lots
of pictures), and has a couple immediate applications. I will finish
by briefly mentioning current work modifying of this combinatorics in
various ways, and connecting the combinatorics to geometric
realizations of the crystals using Nakajima's quiver varieties.