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| Format: | Preprint |
| Published: |
2011
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| Online Access: | https://arxiv.org/abs/1107.2833 |
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| _version_ | 1866915711501205504 |
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| author | Oshima, Yoshiki |
| author_facet | Oshima, Yoshiki |
| contents | In this article, we study the restriction of Zuckerman's derived functor (g,K)-modules A_q(λ) to g' for symmetric pairs of reductive Lie algebras (g,g'). When the restriction decomposes into irreducible (g',K')-modules, we give an upper bound for the branching law. In particular, we prove that each (g',K')-module occurring in the restriction is isomorphic to a submodule of A_q'(λ') for a parabolic subalgebra q' of g', and determine their associated varieties. For the proof, we construct A_q(λ) on complex partial flag varieties by using D-modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1107_2833 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | On the restriction of Zuckerman's derived functor modules A_q(λ) to reductive subgroups Oshima, Yoshiki Representation Theory 22E46 (Primary) 14F10, 32C38 (Secondary) In this article, we study the restriction of Zuckerman's derived functor (g,K)-modules A_q(λ) to g' for symmetric pairs of reductive Lie algebras (g,g'). When the restriction decomposes into irreducible (g',K')-modules, we give an upper bound for the branching law. In particular, we prove that each (g',K')-module occurring in the restriction is isomorphic to a submodule of A_q'(λ') for a parabolic subalgebra q' of g', and determine their associated varieties. For the proof, we construct A_q(λ) on complex partial flag varieties by using D-modules. |
| title | On the restriction of Zuckerman's derived functor modules A_q(λ) to reductive subgroups |
| topic | Representation Theory 22E46 (Primary) 14F10, 32C38 (Secondary) |
| url | https://arxiv.org/abs/1107.2833 |