Stability in Modules for Classical Lie Algebras: A Constructive Approach (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

Benkart, Georgia M.; Britten, D. J.; Lemire, F. W.

Softcover

ISBN 10: 0821824929 ISBN 13: 9780821824924

Publisher: American Mathematical Society, 1992

Synopsis

During the last century, mathematicians and physicists alike have studied extensively the finite dimensional irreducible representations of complex classical Lie algebras. These studies have led to numerous formulas for computing the dimensions, weights, weight multiplicities, and tensor products of the representations. The dependence of these quantities on the rank of the Lie algebra has been revealed in recent investigations using Schur functions and characters.

About this title

Synopsis

During the last century, mathematicians and physicists alike have studied extensively the finite dimensional irreducible representations of complex classical Lie algebras. These studies have led to numerous formulas for computing the dimensions, weights, weight multiplicities, and tensor products of the representations. The dependence of these quantities on the rank of the Lie algebra has been revealed in recent investigations using Schur functions and characters. This book develops a constructive approach to the rank dependence, beginning from Hermann Weyl's realization of the module inside a certain M-fold tensor product of the natural representation. New proofs are derived for some of the more difficult aspects of Weyl's construction, especially those involving contraction maps. The explicit structural information about weights and maximal vectors obtained here show that the rank dependence and stability of the modules occur not just on a character level, but occur because the structure of the modules and their tensor products is basically the same in each case.

For those having some familiarity with Lie algebras and their representations, the book provides sufficient background to make the monograph self-contained.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1992
• Language: English
• ISBN 10: 0821824929
• ISBN 13: 9780821824924
• Binding: Paperback
• Number of pages: 165