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Lie Groups and Representation Theory Seminar

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Date: June 13 (Tue), 2023, 17:00-18:00
Speaker: Yoshiki Oshima (大島芳樹) (The University of Tokyo)
Title: Examples of discrete branching laws of derived functor modules / 導来関手加群の離散分岐則の例
Abstract:
[ pdf ]
We consider the restriction of Zuckerman's derived functor modules for symmetric pairs of real reductive groups assuming that it is discretely decomposable in the sense of Kobayashi. By using a classification result, it can be shown that the restriction decomposes as a direct sum of Zuckerman's derived functor modules for the subgroup. In the last talk, by using the realization of representations as D-modules, a decomposition of Zuckerman's modules corresponding to an orbit decomposition of flag varieties was explained. In this talk, we would like to see that such a decomposition can be written as a direct sum of Zuckerman's modules of the subgroup in some concrete examples.

実簡約Lie群の対称対に関するZuckerman導来関手加群の制限を考える.小林俊行 氏によって導入された離散分解の仮定の下で,制限は部分群に対するZuckerman加 群の直和に分解することが分類の結果を用いて示される.前回の講演ではD加群と しての表現の実現を用いて旗多様体の軌道分解に対応したZuckerman加群の分解に ついて説明した.今回はそのような分解が部分群のZuckerman加群の直和に書き換 えられることを具体例に沿ってお話ししたい.

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