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THE COINVARIANT ALGEBRA AND REPRESENTATION TYPES OF BLOCKS OF CATEGORY O

Published online by Cambridge University Press:  28 November 2001

TH. BRÜSTLE ,
S. KÖNIG  and
V. MAZORCHUK
TH. BRÜSTLE
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501, Bielefeld, FRG; bruestle@mathematik.uni-bielefeld.de, koenig@mathematik.uni-bielefeld.de
S. KÖNIG
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501, Bielefeld, FRG; bruestle@mathematik.uni-bielefeld.de, koenig@mathematik.uni-bielefeld.de Present address: Department of Mathematics and Computer Science, University of Leicester, Leicester, LE1 7RH; sck5@mcs.le.ac.uk
V. MAZORCHUK
Affiliation:
Algebra, Mechanics and Mathematics Department, Kyiv Taras Shevchenko University, 64 Volodymyrska st., 01033, Kyiv, Ukraine; mazor@mechmat.univ.kiev.ua Present address: Department of Mathematics, Uppsala University, Box 480, SE-75106, Sweden; mazor@math.uu.se
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Abstract

Let [Gfr ] 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 [Oscr] . By results of Soergel, A has a combinatorial description in terms of a subalgebra C0 of the coinvariant algebra C. König and Mazorchuk have constructed an embedding from C0-mod into the category [Fscr](Δ) of A-modules having a Verma flag. This is the main tool for the classification of [Fscr] (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.

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Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 6 , November 2001 , pp. 669 - 681
Copyright
© The London Mathematical Society 2001

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