The Quantum Linear Groups (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

Parshall, Brian; Wang, Jian-Pan

Softcover

ISBN 10: 0821825011 ISBN 13: 9780821825013

Publisher: American Mathematical Society, 1992

Synopsis

This volume begins with a general discussion of the theory of quantum groups. The authors view the theory as a natural extension of the theory of affine group schemes. They establish a number of foundational results, including the theory of induced representations and spectral sequences for quantum group cohomology. They then apply these results to give a detailed study on the quantum general linear group and its representation theory. Some of the central topics included are a
development of quantum determinants, Frobenius kernals and their representation theory, high weight theory, and the generalization of various important theorems concerning the cohomology of vector bundles on the flag manifold. Finally, the authors use the theory to give a treatment of q-Schur algebras, proving, for example, that q-Schur algebras are quasi-hereditary.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1992
• Language: English
• ISBN 10: 0821825011
• ISBN 13: 9780821825013
• Binding: Paperback