By Alexander Kleshchev

ISBN-10: 0521104181

ISBN-13: 9780521104180

The illustration concept of symmetric teams is likely one of the most lovely, well known, and critical elements of algebra with many deep kinfolk to different parts of arithmetic, comparable to combinatorics, Lie concept, and algebraic geometry. Kleshchev describes a brand new method of the topic, in line with the hot paintings of Lascoux, Leclerc, Thibon, Ariki, Grojnowski, Brundan, and the writer. a lot of this paintings has simply seemed within the learn literature ahead of. despite the fact that, to make it available to graduate scholars, the speculation is constructed from scratch, the one prerequisite being a customary path in summary algebra. Branching principles are in-built from the outset leading to a proof and generalization of the hyperlink among modular branching ideas and crystal graphs for affine Kac-Moody algebras. The tools are in simple terms algebraic, exploiting affine and cyclotomic Hecke algebras. For the 1st time in publication shape, the projective (or spin) illustration idea is taken care of alongside a similar strains as linear illustration thought. the writer is especially involved in modular illustration conception, even if every little thing works in arbitrary attribute, and in case of attribute zero the process is a bit of just like the idea of Okounkov and Vershik, defined right here in bankruptcy 2. For the sake of transparency, Kleshschev concentrates on symmetric and spin-symmetric teams, even though the equipment he develops are really common and observe to a couple of similar items. In sum, this special e-book could be welcomed by way of graduate scholars and researchers as a contemporary account of the topic.