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Bibliografische Details

Titel: Quantum Linear Groups (Memoirs of the American Mathematical Society 439)
Verlag: American Mathematical Society
Erscheinungsjahr: 1991
Sprache: Englisch
ISBN-10: 0821825011
ISBN-13: 9780821825013
Einband: Softcover
Zustand: Fine

�ber diesen Titel

Inhaltsangabe

Este volumen comienza con una discusi�n general de la teor�a de los grupos cu�nticos. Los autores ven la teor�a como una extensi�n natural de la teor�a de los esquemas de grupos afines. Establecen una serie de resultados fundamentales, incluida la teor�a de representaciones inducidas y secuencias espectrales para la cohomolog�a de grupos cu�nticos. Luego aplican estos resultados para dar un estudio detallado sobre el grupo lineal general cu�ntico y su teor�a de representaci�n. Algunos de los temas centrales incluidos son
desarrollo de determinantes cu�nticos, n�cleos de Frobenius y su teor�a de representaci�n, teor�a de alto peso y la generalizaci�n de varios teoremas importantes relacionados con la cohomolog�a de los haces de vectores en el colector de banderas. Finalmente, los autores utilizan la teor�a para dar un tratamiento de las �lgebras q-Schur, demostrando, por ejemplo, que las �lgebras q-Schur son cuasi hereditarias.

Rese�a del editor

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.

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