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Hecke Algebras with Unequal Parameters
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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 on the properties of Hecke algebras with unequal parameters and presents examples verifying these conjectures.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, inCoxeter groups; Partial order on W; The algebra {mathcal H...
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 on the properties of Hecke algebras with unequal parameters and presents examples verifying these conjectures.
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
Coxeter groups; Partial order on W; The algebra {mathcal H}; The bar operator; The elements c w; Left or right multiplication by c s; Dihedral groups; Cells; Cosets of parabolic subgroups; Inversion; The longest element for a finite W; Examples of elements D w; The function mathbf{a}; Conjectures; Example: The split case; Example: The quasisplit case; Example: The infinite dihedral case; The ring J; Algebras with trace form; The function {mathbf{a}} E; Study of a left cell; Constructible representations; Two-sided cells; Virtual cells; Relative Coxeter groups; Representations; A new realization of Hecke algebras; Bibliography; Other titles in this series
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
Coxeter groups; Partial order on W; The algebra {mathcal H}; The bar operator; The elements c w; Left or right multiplication by c s; Dihedral groups; Cells; Cosets of parabolic subgroups; Inversion; The longest element for a finite W; Examples of elements D w; The function mathbf{a}; Conjectures; Example: The split case; Example: The quasisplit case; Example: The infinite dihedral case; The ring J; Algebras with trace form; The function {mathbf{a}} E; Study of a left cell; Constructible representations; Two-sided cells; Virtual cells; Relative Coxeter groups; Representations; A new realization of Hecke algebras; Bibliography; Other titles in this series