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The Coinvariant Algebra and Representation Types of Blocks of Category O
Author(s) -
Brüstle Th.,
Konig S.,
Mazorchuk V.
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609301008529
Subject(s) - mathematics , subalgebra , verma module , representation (politics) , representation theory , algebra over a field , embedding , pure mathematics , block (permutation group theory) , type (biology) , combinatorics , lie algebra , artificial intelligence , computer science , ecology , politics , political science , law , biology
Let G be a finite‐dimensional semisimple Lie algebra over the complex numbers. Let A be the finite‐dimensional algebra of a (regular or singular) block of the BGG‐category O. By results of Soergel, A has a combinatorial description in terms of a subalgebra C 0 of the coinvariant algebra C . König and Mazorchuk have constructed an embedding from C 0 ‐mod into the category F(Δ) of A ‐modules having a Verma flag. This is the main tool for the classification of F(Δ) into finite, tame and wild representation types presented here. As a consequence a classification of A ‐mod into finite, tame and wild representation types is obtained, thus re‐proving a recent result of Futorny, Nakano and Pollack. 2000 Mathematics Subject Classification 16G60, 17B10.