Khare, Apoorva (2005) Category O over a deformation of the symplectic oscillator algebra Journal of Pure and Applied Algebra, 195 (2). pp. 131-166. ISSN 0022-4049
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Official URL: http://doi.org/10.1016/j.jpaa.2004.06.004
Related URL: http://dx.doi.org/10.1016/j.jpaa.2004.06.004
Abstract
We discuss the representation theory of Hf, which is a deformation of the symplectic oscillator algebra , where is the ((2n+1)-dimensional) Heisenberg algebra. We first look at a more general algebra with a triangular decomposition. Assuming the PBW theorem, and one other hypothesis, we show that the BGG category is abelian, finite length, and self-dual. We decompose as a direct sum of blocks , and show that each block is a highest weight category. In the second part, we focus on the case Hf for n=1, where we prove all these assumptions, as well as the PBW theorem.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier B.V. |
| ID Code: | 127297 |
| Deposited On: | 17 Oct 2022 05:13 |
| Last Modified: | 17 Oct 2022 05:13 |
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