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Representation Theory of Reductive Normal Algebraic Monoids
Author(s):
Stephen
Doty
Journal:
Trans. Amer. Math. Soc.
351
(1999),
2539-2551.
MSC (1991):
Primary 20G05, 20M30;
Secondary 16G99, 22E55
Posted:
February 15, 1999
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Abstract:
New results in the representation theory of ``semisimple'' algebraic monoids are obtained, based on Renner's monoid version of Chevalley's big cell. (The semisimple algebraic monoids have been classified by Renner.) The rational representations of such a monoid are the same thing as ``polynomial'' representations of the associated reductive group of units in the monoid, and this representation category splits into a direct sum of subcategories by ``homogeneous'' degree. We show that each of these homogeneous subcategories is a highest weight category, in the sense of Cline, Parshall, and Scott, and so equivalent with the module category of a certain finite-dimensional quasihereditary algebra, which we show is a generalized Schur algebra in S. Donkin's sense.
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Additional Information:
Stephen
Doty
Affiliation:
Mathematical and Computer Sciences, Loyola University of Chicago, Chicago, Illinois 60626
Email:
doty@math.luc.edu
DOI:
10.1090/S0002-9947-99-02462-9
PII:
S 0002-9947(99)02462-9
Received by editor(s):
June 26, 1996
Posted:
February 15, 1999
Additional Notes:
Partially supported by NSF grant DMS-9401576
Copyright of article:
Copyright
1999,
American Mathematical Society
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