Irreducible unitary representations with non-zero relative Lie algebra cohomology of the Lie group SO₀(2,m)

2023/09/22 by Ankita Pal, Pal, Ankita, Pampa Paul +1 · 1 citation
Mathematics · #17B10 #17B20 #17B22 #17B56 #22E46 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2309.12703

openalex publication_date 2023/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

By a theorem of D. Wigner, an irreducible unitary representation with non-zero (\frakg,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 Poincaré polynomial of cohomologies of these representations for the Lie group SO₀(2,m) for any positive integer m. We have also determined, among these, which are discrete series representations and holomorphic discrete series representations.

Cited by

• Special cycles in compact locally Hermitian symmetric spaces of type III associated with the Lie group SO₀(2,m)

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