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Quantum Deformations of Imaginary Verma Modules |
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| Authors: | Cox B; Futorny V; Kang S-J; Melville D |
| Institution: | Department of Mathematical Sciences, University of Montana Missoula, Montana 59812-1032, USA. Email: ma_blc{at}selway.umt.edu Department of Mathematics, Kiev University Kiev 252617, Ukraine. Email: foutorny{at}qucdn.queensu.ca Department of Mathematics, College of Natural Sciences, Seoul National University Seoul 151-742, Republic of Korea. Email sjkang{at}math.snu.ac.kr Department of Mathematics, St Lawrence University Canton, NY 13617, USA. Email: dmel{at}music.stlawu.edu |
| Abstract: | We construct quantum deformations of imaginary Verma modulesover  and show that, for generic q, imaginary Verma modules over can be deformed to those over the quantum group  in such a way that the dimensions of the weightspaces are invariant under the deformation. We also prove thePBW theorem for with respect to the triangular decomposition induced from the root partitioncorresponding to the imaginary Verma modules. 1991 MathematicsSubject Classification: 17B67, 17B65, 17B10. |
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