This quantity includes the court cases of the overseas Congress of Mathematicians satellite tv for pc convention on Algebraic and Combinatorial techniques to illustration idea, held August 12-16, 2010, on the nationwide Institute of complicated reports, Bangalore, India, and the follow-up convention held may perhaps 18-20, 2012, on the collage of California, united states. It includes unique learn and survey articles on quite a few issues within the conception of representations of Lie algebras, quantum teams and algebraic teams, together with crystal bases, categorification, toroidal algebras and their generalisations, vertex algebras, Hecke algebras, Kazhdan-Lusztig bases, $q$-Schur algebras, and Weyl algebras.
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