The General Setting

This chapter contains sections titled: Introduction, Preliminary Survey, A Simple Artificial Adaptive System, A Complex Natural Adaptive System, Some General Observations

[1]  J. Van der Jeugt,et al.  On the composition factors of Kac modules for the Lie superalgebras sl(m/n) , 1992 .

[2]  P. Roman,et al.  Symmetry in Physics , 1969 .

[3]  Minoru Wakimoto,et al.  Integrable Highest Weight Modules over Affine Superalgebras and Number Theory , 1994 .

[4]  Alfredo Capelli.  Lezioni sulla teoria delle forme algebriche , 1902 .

[5]  Claudio Procesi,et al.  A characteristic free approach to invariant theory , 1976 .

[6]  Adriano M. Garsia,et al.  Relations between Young's natural and the Kazhdan-Lusztig representations of Sn , 1988 .

[7]  Jacob Towber.  Two new functors from modules to algebras , 1977 .

[8]  A Brini,et al.  Capelli's theory, Koszul maps, and superalgebras. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[9]  D. Eisenbud,et al.  Young diagrams and determinantal varieties , 1980 .

[10]  Jacques Deruyts.  Essai d'une théorie générale des formes algébriques , 1890 .

[11]  G C Rota,et al.  Standard basis in supersymplectic algebras. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Amitai Regev,et al.  Hook young diagrams with applications to combinatorics and to representations of Lie superalgebras , 1987 .

[13]  A Brini,et al.  Gordan-Capelli series in superalgebras. , 1988, Proceedings of the National Academy of Sciences of the United States of America.

[14]  M. Marcus.  Finite dimensional multilinear algebra , 1973 .

[15]  David A. Buchsbaum,et al.  Schur Functors and Schur Complexes , 1982 .

[16]  Yuval Ne'eman,et al.  Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry) , 1975 .

[17]  Itzhak Bars,et al.  Dimension and Character Formulas for Lie Supergroups , 1981 .

[18]  Gian-Carlo Rota,et al.  On the Foundations of Combinatorial Theory: IX Combinatorial Methods in Invariant Theory , 1974 .

[19]  J. A. Green,et al.  Classical Invariants and the General Linear Group , 1991 .

[20]  Jacques Désarménien.  An algorithm for the rota straightening formula , 1980, Discret. Math..

[21]  M. Scheunert,et al.  The Theory of Lie Superalgebras: An Introduction , 1979 .

[22]  D. Kazhdan,et al.  Representations of Coxeter groups and Hecke algebras , 1979 .

[23]  Amitai Regev,et al.  Hook young diagrams, combinatorics and representations of Lie superalgebras , 1983 .

[24]  Victor G. Kac,et al.  Representations of classical lie superalgebras , 1978 .

[25]  Charles W. Curtis.  Pioneers of representation theory , 1962 .

[26]  Victor G. Kac,et al.  Characters of typical representations of classical lie superalgebras , 1977 .

[27]  G C Rota,et al.  Supersymmetric Hilbert space. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[28]  T. Inui,et al.  The Symmetric Group , 1990 .

[29]  James Green,et al.  Polynomial representations of GLn , 1980 .

[30]  I. G. MacDonald,et al.  Symmetric functions and Hall polynomials , 1979 .

[31]  Alfred Young,et al.  The collected papers of Alfred Young 1873-1940 , 1977 .

[32]  J. Dieudonne,et al.  Invariant theory, old and new , 1971 .

[33]  Michael Clausen.  Letter Place Algebras and a Characteristic-Free Approach to the Representation Theory of the General Linear and Symmetric Groups, I , 1979 .

[34]  R. Carter.  Lie Groups , 1970, Nature.

[35]  Andrew H. Wallace.  Invariant Matrices and the Gordan-Capelli Series , 1952 .

[36]  Vera Serganova,et al.  Generic Irreducible Representations of Finite-Dimensional Lie Superalgebras , 1994 .

[37]  R. Howe,et al.  Remarks on classical invariant theory , 1989 .

[38]  Bruce E. Sagan,et al.  The symmetric group - representations, combinatorial algorithms, and symmetric functions , 2001, Wadsworth & Brooks / Cole mathematics series.

[39]  F. D. Grosshans.  The Symbolic Method and Representation Theory , 1993 .

[40]  Gian-Carlo Rota,et al.  On the foundations of combinatorial theory III , 1969 .

[41]  Peter D. Jarvis,et al.  Diagram and superfield techniques in the classical superalgebras , 1981 .

[42]  Gian-Carlo Rota,et al.  Invariant theory and superalgebras , 1987 .

[43]  L. M. M.-T..  The Theory of Determinants, Matrices and Invariants , 1929, Nature.

[44]  I. Gel'fand,et al.  Structure of representations generated by vectors of highest weight , 1971 .

[45]  Joseph P. S. Kung,et al.  Invariant theory, Young bitableaux, and combinatorics , 1978 .

[46]  Andrea Brini,et al.  Remark on the Branching theorem and supersymmetric algebras , 1991 .

[47]  Hermann Boerner,et al.  Über die rationalen Darstellungen der allgemeinen linearen Gruppe , 1948 .

[48]  T. B.,et al.  The Theory of Determinants , 1904, Nature.

[49]  A Brini,et al.  Capelli bitableaux and Z-forms of general linear Lie superalgebras. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[50]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[51]  Gian-Carlo Rota,et al.  On the Exterior Calculus of Invariant Theory , 1985 .

[52]  B. Kostant,et al.  Graded manifolds, graded Lie theory, and prequantization , 1977 .

[53]  A Brini,et al.  Young-Capelli symmetrizers in superalgebras. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[54]  A. Brini,et al.  The umbral symbolic method for supersymmetric tensors , 1992 .

[55]  D. G. Mead,et al.  Determinantal ideals, identities, and the Wronskian. , 1972 .