Irreducible unitary representations with non-zero relative Lie algebra cohomology of the Lie group $SO_0(2,m)$
| Autor: | Pal, Ankita, Paul, Pampa |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | By a theorem of D. Wigner, an irreducible unitary representation with non-zero $(\frak{g},K)$-cohomology has trivial infinitesimal character, and hence up to unitary equivalence, these are finite in number. We have determined the number of equivalence classes of these representations and the Poincar\'{e} polynomial of cohomologies of these representations for the Lie group $SO_0(2,m)$ for any positive integer $m.$ We have also determined, among these, which are discrete series representations and holomorphic discrete series representations. Comment: 20 pages, 2 figures |
| Databáze: | arXiv |
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