In mathematics, Matsushima's formula, introduced by Matsushima (1967), is a formula for the Betti numbers of a quotient of a symmetric space G/H by a discrete group, in terms of unitary representations of the group G. [1] The Matsushima–Murakami formula is a generalization giving dimensions of spaces of automorphic forms, introduced by Matsushima & Murakami (1968).[2]

References

  1. ↑ Matsushima, Yozô (1967), "A formula for the Betti numbers of compact locally symmetric Riemannian manifolds", Journal of Differential Geometry, 1 (1–2): 99–109, doi:10.4310/jdg/1214427883, ISSN 0022-040X, MR 0222908, S2CID 117292003
  2. ↑ Matsushima, Yozô; Murakami, Shingo (1968), "On certain cohomology groups attached to Hermitian symmetric spaces. II", Osaka Journal of Mathematics, 5: 223–241, ISSN 0030-6126, MR 0266238


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