Irreducible unitary representations with non-zero relative Lie algebra cohomology of the Lie group $SO_0(2,m)$

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发表日期：

2025年5月3日

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Ankita Pal,
Pampa Paul

摘要

By a result of D. Wigner, an irreducible unitary representation with non-zero $(\mathfrak {g},K)$ $(g, K)$ -cohomology has trivial infinitesimal character, and hence up to unitary equivalence, these are finite in number, by a result of Harish-Chandra. We have determined the number of equivalence classes of these representations and the Poincaré-Hodge polynomials of cohomologies of these representations for the Lie group $S{O_0}(2,m)$ $S O_{0} (2, m)$ for any positive integer m. We have also determined, among these, which are discrete series representations and holomorphic discrete series representations.

Irreducible unitary representations with non-zero relative Lie algebra cohomology of the Lie group \(SO_0(2,m)\)

摘要