Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. Without specializing in a small number of subject areas, it emphasizes the most active and influential areas of current mathematics.

### Volume 93, Number 1

#### Publication Date: 15 May 1998

Affine Hecke algebras and raising operators for Macdonald polynomials

Anatol N. Kirillov and Masatoshi Noumi; 1-39

Highest weight modules over the $W_{1+\infty}$ algebra and the bispectral problem

B. Bakalov, E. Horozov and M. Yakimov; 41-72

An analogue of the Hom functor and a generalized nuclear democracy theorem

Haisheng Li; 73-114

Subelliptic estimates for the $\overline{\partial}$-Neumann operator on piecewise smooth strictly pseudoconvex domains

Joachim Michel and Mei-Chi Shaw; 115-128

Modular moonshine, III

Richard E. Borcherds; 129-154

The stable $4$-dimensional geometry of the real Grassmann manifolds

Weiqing Gu; 155-178

The relative log Poincaré lemma and relative log de Rham theory

Fumiharu Kato; 179-206