Biographies of James Lepowsky and Robert Wilson
James Lepowsky was born on July 5, 1944 in New York City. He attended
Stuyvesant High School and then Harvard College, 1961-65, where Shlomo Stern-
berg introduced him to Lie groups and encouraged him to go to M.I.T. and learn
about Lie theory from Bertram Kostant. At M.I.T., Lepowsky decided very soon
to study with Kostant, and he received his Ph.D. in 1970 under the joint direction
of Sigurdur Helgason and Bertram Kostant. His thesis involved representations of
real rank one groups, branching laws and minimal K-types.
Lepowsky was a lecturer and research associate at Brandeis University from 1970
to 1972. Around this time, he collaborated with Gerald McCollum and with Nolan
Wallach on problems in Lie theory and representation theory. He was an assistant
professor at Yale University from 1972 to 1977, including a year as a Yale Junior
Faculty Fellow at the Institute for Advanced Study, where he has also been a mem-
ber during four other periods. At Yale he initiated a study of the structure of
"generalized Verma modules" and he developed generalizations of the Bernstein-
Gelfand-Gelfand resolution. Howard Garland stimulated Lepowsky's interest in
Macdonald's identities and homology. Using the results of collaborations with Gar-
land, Stephen Milne and Alex Feingold at Yale, Lepowsky began collaborating
with Robert Wilson, who was on leave from Rutgers in 1976-77, on what became
twisted vertex operator realizations of affine Lie algebras and structures they called
"Z-algebras," with applications to partition identities.
After lecturing at Universite Paris VI in 1978 during the second year of a Sloan
Fellowship, Lepowsky began teaching at Rutgers, where he continued collaborating
with Wilson, and where, with Arne Meurman, his first Ph.D. student, he began
working on what became a collaboration with Igor Frenkel and Meurman on the
construction of a "moonshine module" for the Monster group, based on a new
algebra of vertex operators. Some of this work was done when Frenkel, Lepowsky
and Meurman were at the Mathematical Sciences Research Institute in 1983-84, and
their monograph on this work was completed while the authors were at the Institute
for Advanced Study in 1987-88, at which time Lepowsky was a Guggenheim Fellow.
Lepowsky has also written monographs with Mirko Prime; with Frenkel and Yi-Zhi
Huang, his Rutgers colleague and former student; with Chongying Dong; and with
his and Wilson's former student Haisheng Li. Huang and Lepowsky have developed
a tensor category theory for suitable classes of modules for a vertex operator alge-
bra. Most of Lepowsky's recent work involves the representation theory of vertex
operator algebras and applications.
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