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Representations of Affine Hecke Algebras: Lecture Notes in Mathematics, cartea 1587

Autor Nanhua XI
en Limba Engleză Paperback – 26 sep 1994
Kazhdan and Lusztig classified the simple modules of an affine Hecke algebra Hq (q E C*) provided that q is not a root of 1 (Invent. Math. 1987). Ginzburg had some very interesting work on affine Hecke algebras. Combining these results simple Hq-modules can be classified provided that the order of q is not too small. These Lecture Notes of N. Xi show that the classification of simple Hq-modules is essentially different from general cases when q is a root of 1 of certain orders. In addition the based rings of affine Weyl groups are shown to be of interest in understanding irreducible representations of affine Hecke algebras. Basic knowledge of abstract algebra is enough to read one third of the book. Some knowledge of K-theory, algebraic group, and Kazhdan-Lusztig cell of Cexeter group is useful for the rest
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Specificații

ISBN-13: 9783540583899
ISBN-10: 3540583890
Pagini: 152
Ilustrații: VIII, 144 p.
Dimensiuni: 155 x 235 x 8 mm
Greutate: 0.49 kg
Ediția:1994
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seriile Lecture Notes in Mathematics, Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn

Locul publicării:Berlin, Heidelberg, Germany

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Research

Descriere

Kazhdan and Lusztig classified the simple modules of an affine Hecke algebra Hq (q E C*) provided that q is not a root of 1 (Invent. Math. 1987). Ginzburg had some very interesting work on affine Hecke algebras. Combining these results simple Hq-modules can be classified provided that the order of q is not too small. These Lecture Notes of N. Xi show that the classification of simple Hq-modules is essentially different from general cases when q is a root of 1 of certain orders. In addition the based rings of affine Weyl groups are shown to be of interest in understanding irreducible representations of affine Hecke algebras. Basic knowledge of abstract algebra is enough to read one third of the book. Some knowledge of K-theory, algebraic group, and Kazhdan-Lusztig cell of Cexeter group is useful for the rest

Cuprins

Hecke algebras.- Affine Weyl groups and affine Hecke algebras.- A generalized two-sided cell of an affine Weyl group.- qs-analogue of weight multiplicity.- Kazhdan-Lusztig classification on simple modules of affine Hecke algebras.- An equivalence relation in T × ?*.- The lowest two-sided cell.- Principal series representations and induced modules.- Isogenous affine Hecke algebras.- Quotient algebras.- The based rings of cells in affine Weyl groups of type .- Simple modules attached to c 1.