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Hecke Algebras of Classical Type and Their Representation Type
Author(s) -
Ariki Susumu
Publication year - 2005
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611505015236
Subject(s) - mathematics , type (biology) , representation (politics) , pure mathematics , representation theory , hecke operator , algebra over a field , hecke algebra , mathematics subject classification , modular form , ecology , politics , political science , law , biology
The purpose of this article is to determine the representation type for all of the Hecke algebras of classical type. To do this, we combine methods from our previous work, which is used to obtain information on their Gabriel quivers, and recent advances in the theory of finite‐dimensional algebras. The principal computation is for Hecke algebras of type B with two parameters. Then, we show that the representation type of Hecke algebras is governed by their Poincaré polynomials. 2000 Mathematics Subject Classification 20C08, 20G05, 33D80.