In mathematics, Blattner's conjecture or Blattner's formula is a description of the discrete series representations of a general semisimple group G in terms of their restricted representations to a maximal compact subgroup K (their so-called K-types).
Blattner's formula says that if a discrete series representation with infinitesimal character λ is restricted to a maximal compact subgroup K, then the representation of K with highest weight μ occurs with multiplicity where Blattner's formula is what one gets by formally restricting the Harish-Chandra character formula for a discrete series representation to the maximal torus of a maximal compact group.
In this case the character is a distribution on the maximal compact subgroup with support on the singular elements.
Blattner's conjecture (formula) was also proved by Enright (1979) by infinitesimal methods which were totally new and completely different from those of Hecht and Schmid (1975).
Enright (1978) used his ideas to obtain results on the construction and classification of irreducible Harish-Chandra modules of any real semisimple Lie algebra.