A solution of Warner's 3rd problem for representations of holomorphic type

Author:
Floyd L. Williams

Journal:
Trans. Amer. Math. Soc. **293** (1986), 605-612

MSC:
Primary 22E46; Secondary 11F70, 32M15

DOI:
https://doi.org/10.1090/S0002-9947-1986-0816313-2

MathSciNet review:
816313

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Abstract: In response to one of ten problems posed by G. Warner, we assign (to the extent that it is possible) a geometric or cohomological interpretation-- in the sense of Langlands--to the multiplicty in of an irreducible unitary representation of a semisimple Lie group , where is a discrete subgroup of , in the case when has a highest weight.

**[1]**H. Fischer and F. Williams,*Borel-Le Potier diagrams--calculus of their cohomology bundles*, Tôhoku Math. J.**36**(1984), 233-251. MR**742597 (86c:32033)****[2]**P. Griffiths and W. Schmid,*Locally homogeneous complex manifolds*, Acta Math.**123**(1969), 253-302. MR**0259958 (41:4587)****[3]**R. Langlands,*Dimension of spaces of automorphic forms*, Proc. Sympos. in Pure Math., Vol. 9, Amer. Math. Soc., Providence, R.I., 1966, pp. 253-257. MR**0212135 (35:3010)****[4]**R. Parthasarathy,*Criteria for the unitarizability of some highest weight modules*, Proc. Indian Acad. Sci.**89**(1980), 1-24. MR**573381 (82c:22020)****[5]**W. Schmid,*On a conjecture of Langlands*, Ann. of Math. (2)**93**(1971), 1-42. MR**0286942 (44:4149)****[6]**G. Warner,*Selberg's trace formula for nonuniform lattices*:*The*-*rank one case*, Advances in Math., Suppl. Studies, 6, Academic Press, New York, 1979, pp. 1-142. MR**535763 (81f:10044)****[7]**F. Williams,*Vanishing theorems for type**cohomology of locally symmetric spaces*(I), Osaka J. Math.**18**(1981), 147-160. MR**609983 (82k:22013)****[8]**-,*An alternating sum formula for the multiplicities of unitary highest weight modules in*, unpublished manuscript.**[9]**-,*Discrete series multiplicities in*(II):*Proof of Langlands' conjecture*, Amer. J. Math.**107**(1985), 367-376. MR**784287 (86h:22025)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1986-0816313-2

Article copyright:
© Copyright 1986
American Mathematical Society