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References
I.N. Bernstein, I.M. Gelfand, S.I. Gelfand, Schubert cells and cohomology of the spaces G/P, Russian Math. Surveys 28, 3 (1973), 1–26.
T. Brylawski, The lattice of integer partitions, Discrete Math. 6 (1973), 201–219.
M. Gerstenhaber, On dominance and varieties of commuting matrices, Ann. of Math. 73 (1961), 324–348.
A. Grothendieck, Sur la classification des fibrés holomorphes sur la sphère de Riemann, Amer. J. Math. 79 (1957), 121–138.
L. Harper, G.-C. Rota, Matching theory: an introduction, In: P. Ney (ed.), Advances in Probability Vol. 1, Marcel Dekker, 1971, 171–215.
M. Hazewinkel, T. Vorst, On the Snapper, Liebler-Vitale, Lam theorem on permutation representations of the symmetric groups, in preparation.
M. Hazewinkel, C. Martin, Representations of the symmetric group, the specialization order, systems and Grassmann manifolds, in preparation.
W. Hesselink, Singularities in the nilpotent scheme of a classical group, Trans. Amer. Math. Soc. 222 (1976), 1–32.
R.E. Kalman, Kronecker invariants and feedback (+ errata), In: L. Weiss (ed.) Ordinary differential equations, Acad.Pr., 1972, 459–471.
A. Kerber, The diagram lattice as structural principle in mathematics. In: P. Kramers, A. Rieckers (eds.), Group theoretical methods in physics (Tübingen, 1977), Lect.Notes in Physics 79, Springer, 1978, 53–71.
H.P. Kraft, Letter to M. Hazewinkel, June 2, 1980 (This material will be presented at the Torun conference in Sept. 1980).
T.Y. Lam, Young diagrams, Schur functions, the Gale Ryser theorem and a conjecture of Snapper, J. pure and appl. Algebra 10 (1977), 81–94.
R.A. Liebler, M.R. Vitale, Ordening the partition characters of the symmetric group, J. of Algebra 25, (1973), 487–489.
C. Martin, R. Hermann, Applications of algebraic geometry to system theory: the McMillan degree and Kronecker indices of transfer functions as topological an holomorphic system invariants, SIAM J. Control Opt. 16 (1978), 743–755.
A. Mead, E. Ruch, A. Schönhofer, Theory of chirality functions, generalized for molecules with chiral ligands, Theor. Chim. Acta 29 (1973), 269–304.
J. Milnør, J. Stasheff, Characteristic classes, Princeton Univ. Pr., 1974.
E. Ruch, A. Schönhofer, Theorie der Chiralitätsfunktionen, Theor. Chim. Acta 19 (1970), 225–287.
H. Ryser, Combinatorial mathematics, Carus Math. Monographs 14, Wiley, 1963.
S.S. Shatz, The decomposition and specialization of algebraic families of vector bundles, Compositio Math. 35 (1977).
E. Snapper, Group characters and nonnegative integral matrices, J. of Algebra 19 (1971), 520–535.
R.F. Muirhead, Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters, Roc. Edinburgh Math. Soc. 21 (1903), 144–157.
M. Hazewinkel, A partial survey of the uses of algebraic geometry in systems and control theory, Proc. INDAM Vol. 24 (Severi centennial conference, Rome April 1979), Acad.Press, to appear.
M. Hazewinkel, (Fine) moduli spaces in linear system theory: what they are and what they are good for. In C. Martin, C. Byrnes (eds.), Algebraic and geometric methods in linear systems theory, Reidel Publ. Cy, to appear.
J.E. Humphreys, Linear algebraic group, Springer, 1975.
J.C. Jantzen, Moduln met einem höchsten Gewicht, Lect.Notes in Math. 750, Springer, 1979.
J.E. Humphreys, Highest weight modules for semi-simple Lie algebras, In: Proc. Workshop on present trends in representation theory, Carleton Univ., 1979, Lect.Notes Math., Springer, to appear.
A.J. Coleman, Induced representations with applications to Sn, Queen's papers in pure and applied math. 4, Queen's Univ., Kingston, Canada, 1966.
C.W. Curtis, I. Reiner, Representation theory of finite group and associative algebras, Interscience, 1962.
G.D. James, The representation theory of the symmetric groups, Lect. Notes in Math. 682, Springer, 1978.
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Hazewinkel, M. (1981). On representations of the symmetric groups, nilpotent matrices, systems, vectorbundles and Schubert cells. In: Auslander, M., Lluis, E. (eds) Representations of Algebras. Lecture Notes in Mathematics, vol 903. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092990
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DOI: https://doi.org/10.1007/BFb0092990
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