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Crystal Bases: Representations And Combinatorics
This unique book provides the first introduction to crystal base theory from the combinatorial point of view. Crystal base theory was developed by Kashiwara and Lusztig from the perspective of quantum groups. Its power comes from the fact that it addresses many questions in representation theory and mathematical physics by combinatorial means. This book approaches the subject directly from combinatorics, building crystals through local axioms (based on ideas by Stembridge) and virtual crystals. It also emphasizes parallels between the representation theory of the symmetric and general linear groups and phenomena in combinatorics. The combinatorial approach is linked to representation theory through the analysis of Demazure crystals. The relationship of crystals to tropical geometry is also explained.
Directed by Allen Smithee
Allen Smithee specializes in the mediocre. He is versatile. He is prolific. And he doesn't exist. From 1969 until 1999, Allen Smithee was the pseudonym adopted by Hollywood directors when they wished not to be associated with films ostensibly of their making . Encompassing over fifty films of various stripes -- B movies, sequels, music videos, made-for-TV movies -- Smithee's three decades of work affords the authors of this volume a unique opportunity to reassess the claims of auteurism, both in its traditional guise and in the more commodified form it currently assumes. Sometimes treating Smithee as an auteur in much the same way critics and scholars have treated directors as diverse as Dou...
