Schur Algebras of Classical Groups II

REFERENCES

• Beilinson , A. A. , Lusztig , G. , MacPherson , R. ( 1990 ). A geometric setting for the quantum deformation of GL n . Duke Math. J. 61 : 655 – 677 .
   Web of Science ®Google Scholar
• Cline , E. , Parshall , B. , Scott , L. L. ( 1988 ). Finite dimensional algebras and highest weight categories . J. Reine Angew. Math. 391 : 85 – 99 .
   Web of Science ®Google Scholar
• Cline , E. , Parshall , B. , Scott , L. L. (1990). Integral and graded quasi-hereditary algebras I. J. Algebra 131:126–160.
   Google Scholar
• Dipper , R. , Doty , S. ( 2008 ). The rational Schur algebra . Represent. Theory 12 : 58 – 82 .
   Google Scholar
• Donkin , S. ( 1983 ). A note on decomposition numbers for reductive groups . J. Algebra 80 : 226 – 234 .
   Google Scholar
• Donkin , S. ( 1985 ). Rational Representations of Algebraic Groups: Tensor Products and Filtrations . Lecture Notes in Mathematics 1140 . Berlin : Springrt-Verlag .
   Google Scholar
• Donkin , S. ( 1986 ). Schur algebras and related algebras I . J. Algebra 104 : 310 – 328 .
   Google Scholar
• Donkin , S. ( 1987 ). Good filtrations of rational modules for reductive groups . Proceedings of Symposia in Pure Mathematics 47 : 69 – 80 .
   Google Scholar
• Donkin , S. ( 1994 ). Schur algebras and related algebras III: integral representations . Math. Proc. Camb. Phil. Soc. 116 : 37 – 55 .
   Google Scholar
• Doty , S. ( 1998 ). Polynomial representations, algebraic monoids, and Schur algebras of classical type . Journal of Pure and Applied Algebras 123 : 165 – 199 .
   Web of Science ®Google Scholar
• Doty , S. Constructing quantized enveloping algebras via inverse limits of finite dimensional algebras . To appear in J. Algebra , arXiv:math.QA/0711.2764 .
   Google Scholar
• Doty , S. , Hu , J. ( 2009 ). Schur–Weyl duality for orthogonal groups . Proc. London Math. Soc. (3) 98 : 679 – 713 .
   Google Scholar
• Green , J. A. ( 1976 ). Locally finite representations . J. Algebra 41 : 137 – 171 .
   Web of Science ®Google Scholar
• Green , J. A. ( 1980 ). Polynomial Representataions of GL _n . Lecture Notes in Mathematics 830 . Berlin-Heidelberg-New York : Springer-Verlag .
   Google Scholar
• Hayashi , T. ( 1992 ). Quantum deformation of classical groups . Publ. Res. Inst. Math. Sci. 28 : 57 – 81 .
   Google Scholar
• Humphreys , J. E. ( 1972 ). Introduction to Lie Algebras and Representation Theory . Springer, Graduate Texts in Mathematics 9 . New York : Springer-Verlag .
   Google Scholar
• James , G. D. ( 1981 ). On the decomposition matrices of the symmestric groups III . J. Algebra 71 : 115 – 122 .
   Web of Science ®Google Scholar
• Jantzen , J. C. ( 1987 ). Representations of Algebraic Groups . Boston : Academic Press .
   Google Scholar
• Klucznik , M. , Koenig , S. ( 1998 ). Characteristic tilting modules over quasi-hereditary algebras. Course note (from the compact course given in March). Available at http://www.mi.uni-koeln.de/[stilde]koenig/ .
   Google Scholar
• Liu , Q. ( 2006 ). Schur algebras of classical groups . J. Algebra 301 : 867 – 887 .
   Google Scholar
• Oehms , S. ( 1997 ). Symplectic q-Schur algebras. Ph.D. thesis (English version). University of Stuttgart, Shaker Verlag Aachen .
   Google Scholar
• Communicated by C. Cibils.
   Google Scholar