Hecke algebras with unequal parameters / G. Lusztig.

Format:

Book

Author/Creator:

Lusztig, George, 1946- author.

Series:

CRM monograph series ; Volume 18.

CRM Monograph Series ; Volume 18

Language:

English

Subjects (All):

Hecke algebras.

Linear algebraic groups.

Representations of groups.

Physical Description:

1 online resource (138 pages) : illustrations.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2003.

Summary:

Hecke algebras arise in representation theory as endomorphism algebras of induced representations. One of the most important classes of Hecke algebras is related to representations of reductive algebraic groups over $p$-adic or finite fields. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KL-basis) in a Hecke algebra, which is very important in studying relations between representation theory and geometry of the corresponding flag varieties. It turned out that the elements of the KL-basis also possess very interesting combinatorial properties. In the present book, the author extends the theory of the KL-basis to a more general class of Hecke algebras, the so-called algebras with unequal parameters. In particular, he formulates conjectures describing the properties of Hecke algebras with unequal parameters and presents examples verifying these conjectures in particular cases. Written in the author's precise style, the book gives researchers and graduate students working in the theory of algebraic groups and their representations an invaluable insight and a wealth of new and useful information.

Notes:

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-3863-1