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Cohomology of Subregular Tilting Modules for Small Quantum Groups

Published online by Cambridge University Press:  04 December 2007

Viktor Ostrik
Affiliation:
Independent Moscow University,11 Bolshoj Vlasjevskij Per., Moscow 121002 Russia. e-mail: ostrik@mccme.ru
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Abstract

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Let U be a quantumgroup with divid d powers at root ofunity constructed froma root system R .Let u U b th small quantumgroup. The cohomology of u with trivial coefficients was computed by Ginzburg and Kumar. It turns out to be isomorphic to the functions algebra of the nilpotent cone of a semisimpl algebraic group with root system R. In this not we calculate cohomology of u with coefficients in simplest reducible tilting modul with nontrivial cohomology. It appears to b isomorphic to th functions algebra of th closure of the subregular nilpotent orbit.

Type
Research Article
Copyright
© 2002 Kluwer Academic Publishers