Double Affine Hecke Algebras and Congruence Groups

The most general construction of double affine Artin groups (DAAG) and Hecke algebras (DAHA) associates such objects to pairs of compatible reductive group data. We show that DAAG/DAHA It turns out that the structural intricacies of DAAG/DAHA are captured by the underlying We first give a new Coxete...

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Bibliographic Details
Main Authors: Ion, Bogdan, Sahi, Siddhartha
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2021
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Affine algebraic groups
Hecke algebras
Representations of groups
ISBN:1470443260, 9781470443269
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Summary:The most general construction of double affine Artin groups (DAAG) and Hecke algebras (DAHA) associates such objects to pairs of compatible reductive group data. We show that DAAG/DAHA It turns out that the structural intricacies of DAAG/DAHA are captured by the underlying We first give a new Coxeter-type presentation for adjoint DAAG as quotients of the Coxeter braid groups associated to certain crystallographic diagrams that we call double affine Coxeter diagrams. As a consequence we show that the rank two Artin groups of type We show further that the above rank two Artin group action descends to an outer action of the congruence subgroup
Bibliography:November 2020, volume 268, number 1305 (second of 6 numbers)
Includes bibliographical reference (p. 89-90)
ISBN:1470443260
9781470443269
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1305