Preliminary List of Speakers

Mid-Atlantic Algebra Conference


Wake Forest University

Winston-Salem, NC
March 16-17, 2002
 
 
Crystals
 
Arun Ram
University of Wisconsin
 
  A major advance of the 1990s was the development of a new combinatorics for modeling the representations
of complex semisimple Lie algebras. This theory of crystals is a beautiful generalization of combinatorics of boxes and numbers that generally make the subject of "Young tableaux".

These talks will survey the theory of crystals and their connections to other parts of representation theory. The first goal will be to present the basic examples of crystals: representation crystals, the path crystals of Littelmann, Robinson-Schensted crystals, the quiver crystals, and the Fock space crystals of Misra-Miwa. The second goal will be to explain the connections to symmetric functions, canonical bases, Schubert varieties, unipotent orbits, Kazhdan-Lusztig polynomials and the modular representation theory of affine Hecke algebras and symmetric groups.