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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Translation and shuffling of projectively presentable modules and a categorification of a parabolic Hecke module


Authors: Volodymyr Mazorchuk and Catharina Stroppel
Journal: Trans. Amer. Math. Soc. 357 (2005), 2939-2973
MSC (2000): Primary 17B10; Secondary 20C08, 13E10
Published electronically: December 28, 2004
MathSciNet review: 2139933
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Abstract: We investigate certain singular categories of Harish-Chandra bimodules realized as the category of $\mathfrak{p}$-presentable modules in the principal block of the Bernstein-Gelfand-Gelfand category $\mathcal{O}$. This category is equivalent to the module category of a properly stratified algebra. We describe the socles and endomorphism rings of standard objects in this category. Further, we consider translation and shuffling functors and their action on the standard modules. Finally, we study a graded version of this category; in particular, we give a graded version of the properly stratified structure, and use graded versions of translation functors to categorify a parabolic Hecke module.


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Additional Information

Volodymyr Mazorchuk
Affiliation: Department of Mathematics, Uppsala University, Box 480, 751 06, Uppsala, Sweden
Email: mazor@math.uu.se

Catharina Stroppel
Affiliation: Department of Mathematics, Aarhus University, Ny Munkegade 530, 8000 Aarhus C, Denmark
Address at time of publication: Department of Mathematics, University of Glasgow, 15 University Gardens, Glasgow, G12 8QW United Kingdom
Email: stroppel@imf.au.dk, cs@maths.gla.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03650-5
PII: S 0002-9947(04)03650-5
Received by editor(s): January 28, 2004
Published electronically: December 28, 2004
Article copyright: © Copyright 2004 American Mathematical Society