[ Seminar 2023 | Past Seminars | Related conferences etc. ]
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. |
© Toshiyuki Kobayashi