Journal of Lie Theory 17 (2007), No. 1, 073--089
Copyright Heldermann Verlag 2007
A Quantum Analogue of the Bernstein Functor
S. Sinel'shchikov
Inst. Low Temperature Physics Engineering, 47 Lenin Ave., 61103 Kharkov, Ukraine
sinelshchikov@ilt.kharkov.ua
Alexander Stolin
Chalmers Tekniska Högskola, Mathematics, 412 96 Göteborg, Sweden
astolin@math.chalmers.se
L. Vaksman
Inst. Low Temperature Physics Engineering, 47 Lenin Ave., 61103 Kharkov, Ukraine
vaksman@ilt.kharkov.ua
We consider Knapp-Vogan Hecke algebras in the quantum group setting. This allows us to produce a quantum analogue of the Bernstein functor as a first step towards the cohomological induction for quantum groups.
Keywords: Quantum Harish-Chandra modules, cohomological induction, Bernstein functor.
MSC: 17B37, 22E47
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